Prof. dr. habil. Nicolae Popovici

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C U R R I C U L U M    V I T A E

 

Personal data

Name and surname: Nicolae Popovici

Date and place of birth: 03.12.1965, Sighetu-Marmaţiei, Romania

Marital status: Married, two children

Citizenship: Romanian

Present academic position and employer: Professor, Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania

 

Contact information

Work address: 1, M. Kogălniceanu Street, 400084 Cluj-Napoca, Romania

Work phone/fax: +40 264 405 300/+40 264 591 906

E-mail: popovici@math.ubbcluj.ro

 

Education

Habil. Mathematics: March 2016, Babeş-Bolyai University, Cluj-Napoca; thesis title: The role of generalized convexity in vector optimization and related variational problems

Ph.D. Mathematics: June 1995; University of Limoges (France); thesis title: „Contribution à l’optimisation vectorielle”; advisor: Professor Michel Théra

B.S. Mathematics: June 1988; University of Cluj (Romania); dissertation title: „Optimizare Pareto”; advisors: Professor Ioan Maruşciac and Professor Ioan Muntean

 

Languages

Romanian, French, and English; basic knowledge of German, Russian and Ukrainian (dialect, mother tongue)

 

Positions held

2016 -        : professor, Babeş-Bolyai University of Cluj

2007 - 2016: associate professor, Babeş-Bolyai University of Cluj

1994 - 2007: lecturer professor, Babeş-Bolyai University of Cluj; chancellor of the Faculty of Mathematics and Computer Science during 1996-2000

1990 - 1994: assistant professor, Babeş-Bolyai University of Cluj

1988 - 1990: teacher of Mathematics, High School No. 2, Sighetu-Marmaţiei

 

Awards Romanian Academy Award „Spiru Haret” in Mathematical Sciences for 2005 (awarded in December 2007)

 

Courses taught

Calculus, Functional Analysis, Operations Research, Vector Optimization, Decision Theory, Convex Analysis, Multicriteria Optimization (at Universities of Cluj-Napoca, Limoges and Milan), Dynamic Optimization (at University of Varese)

 

Main research interests

Scalar and vector optimization, Convex analysis

 

Visiting appointments abroad and fellowships

 

Sep. 2017: research mobility, University of Halle, Germany

June 2017: research mobility as visiting professor, University of Varese, Italy

May 2017: ERASMUS+ teaching mobility, University of Derby, UK

Mar. 2017: research mobility as visiting professor, University of Varese, Italy

Feb. 2017: research mobility, University of Vienna, Austria

May 2016: ERASMUS+ teaching mobility, University of Derby, UK

Sep. 2015: research mobility, University of Varese, Italy

June 2015: research mobility, University of Milan, Italy

May 2015: ERASMUS+ teaching mobility, University of Derby, UK

Feb. 2015: research mobility, University of Varese, Italy

Sep. 2014: research mobility, University of Varese, Italy

July 2014: research mobility, University of Derby, UK

June 2014: research mobility, University of Varese, Italy

Mar. 2014: research mobility, University of Varese, Italy

Oct. 2013: research mobility, Universities of Derby, UK, Milan, Varese and Pavia, Italy

Sep. 2013: research mobility, Universities of Varese, Italy and Limoges, France

May 2013: research mobility, University of Varese, Italy

Feb. 2013: research mobility as Cariplo visiting professor, University of Varese, Italy

Nov. 2012: research mobility, University of Varese, Italy

June 2012: research mobility, University of Varese, Italy

Apr. 2012: research mobility, Universities of Chemnitz  and Halle, Germany

Dec. 2011: research mobility, University of Varese, Italy

Nov. 2011: research mobility, Universities of Chemnitz  and Halle, Germany

June 2011: research mobility, University of Limoges, France

May 2011: research mobility as Guest fellow, University of Varese, Italy

Sep. 2010: research mobility, University of Varese, Italy

May 2009: research mobility as Guest fellow, University of Varese, Italy

Sep. 2008: research mobility, University of Varese, Italy

Apr. 2008: research & teaching mobility, University of Varese, Italy

Dec. 2007: research & teaching mobility, University of Milan, Italy

Sep. 2007: research mobility, University of Milan, Italy

June - July. 2007: research mobility, University of Limoges, France

Mar. - Apr. 2006: ERASMUS/SOCRATES teaching mobility, University of Limoges, France

Feb. - Mar. 2006: research mobility, Universities of Halle and Chemnitz, Germany

Sep. 2004: invited associate professor, University of Limoges, France

Apr. 2004: ERASMUS/SOCRATES teaching mobility, University of Limoges, France

Sep. 2001: research mobility, University of Limoges, France, supported by CNCSU-Romania & World Bank Grant 46174

Feb. - May 2001: invited associate professor, University of Limoges, France

Dec. 1999: research mobility, University of Limoges, France, supported by CNCSU-Romania & World Bank Grant 46174

May 1999: ERASMUS/SOCRATES teaching mobility, University of Limoges, France

Feb. - June 1998: invited associate professor, University of Limoges, France

Apr. - May 1995: French Government doctoral fellowship (BGF), University of Limoges, France

Feb. - June 1993: invited associate professor, University of Limoges, France

Feb. - July 1992: European Community doctoral fellowship (TEMPUS), University of Saint-Etienne, France

 

Research projects

Director of the Romanian Grant PNII IDEI, Contract 543, CNCSIS code 2261: „Advanced researches on vector and set-valued optimization problems, and variational inequalities under generalized convexity assumptions”, 2009 - 2011. Members of the research team : W. W. Breckner, Şt. Cobzaş, A. Grad, and G. Kassay.

German Research Grant TITELGRUPPE 77: „Multicriteria optimization”, Martin Luther University of Halle (Germany), 2007.

Research project CNCS-UEFISCSU, PN-II-ID-PCE-2011-3-0024; “The structure and sensitivity of the solution sets of variational inequalities, optimization and equilibrium problems under generalized monotonicityˮ, Director: Gábor Kassay, 2011 - 2014.

Romanian Grant CEEX: „Efficient numerical methods with applications on supercomputers”, Contract 2CEX06-11-96 / 19.09.2006, Director: Emil A. Cătinaş, 2006 - 2008.

Romanian Grant CNCSIS type A: „Researches on modern analysis and their applications”, Contracts 148GR/23.05.2006,  34701/2005,  33374/29.06.2004, 33965/8.7.2003, and 33523/17.07.2002,   Director: Wolfgang W. Breckner,  2002 - 2006.

Romanian Grant CNCSIS type A: „Researches of nonlinear applied analysis”, Contract 31400/7053/2001, Director: Wolfgang W. Breckner, 2001.

Romanian Grant CNCSIS type A: „Researches of approximation theory and convex analysis”, Contract 32575/1999, Director: Wolfgang W. Breckner, 1999 - 2000.

International (Romanian, Hungarian, French and Dutch researchers) Grant CNCSU, partially supported by the Word Bank, Contract 46174/27.11.1997, Code 14, „Researches of set-valued analysis with applications in optimization”, Director: Iosif Kolumban, 1997-2000.

Romanian Grant CNCSU: „Researches of approximation theory and convex analysis”, Contracts 16/1998, 7010/1997, 5010/1996, 4010/1995, and 3010/1994, Director: Wolfgang W. Breckner, 1994 - 1998.

 

Other professional activities

Associate editor of: Mathematica (Romanian Academy, Cluj)

Guest editor of: Journal of Global Optimization (Special Issue GCM10 - Vol. 57 (3), 2013)

Referee of: Acta Mathematica Scientia,

Annals of Operations Research

Applied Mathematics and Computation,

Applied Mathematics Letters,

Journal of Applied Mathematics,

Journal of Convex Analysis,

Journal of Global Optimization,

Journal of Industrial and Management Optimization,

Journal of Mathematical Analysis and Applications,

Journal of Optimization Theory and Application,

Nonlinear Analysis: Theory, Methods & Applications,

Operations Research Letters,

Operational Research: An International Journal,

Optimization,

Optimization Letters,

Journal of Numerical Analysis and Approximation Theory (former Revue d'Analyse Numérique et de Théorie de l'Approximation),

Serdica Mathematical Journal,

SIAM Journal on Optimization,

Studia Universitatis Babes-Bolyai, Series Informatica,

Taiwanese Journal of Mathematics,

Yugoslav Journal of Operations Research.

Reviewer of: Zentralblatt für Mathematik,

Mathematical Reviews.

Member of: AMS (American Mathematical Society),

MCDM (International Society on Multiple Criteria Decision Making),

WGGC (Working Group on Generalized Convexity),

SSMR (Romanian Mathematical Society),

EUROPT (The Continuous Optimization Working Group of EURO - Association of European Operational Research Societies).

Director of: Holografica Publishing House, Cluj.

 

 

P U B L I C A T I O N S

 

Books:

1. Breckner, B. E., Popovici, N.: Convexity and Optimization: An Introduction, EFES, Cluj-Napoca, 2006 (202 pages, ISBN 978-973-7677-54-9).

2. Breckner, B. E., Popovici, N.: Problems of Operations Research (in Romanian), EFES, Cluj-Napoca, 2006 (258 pages, ISBN 973-7677-12-9).

3. Popovici, N.: Vector Optimization (in Romanian), Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005 (256 pages, ISBN 973-686-787-0).

4. Breckner, B. E., Popovici, N.: Problems of Convex Analysis in Rn  (in Romanian), Casa Cărţii de Ştiinţă, Cluj-Napoca, 2003 (140 pages, ISBN 973-686-504-5).

 

Book chapters:

1. Lowndes, V., Berry, S., Parkes, C., Bagdasar, O., Popovici, N.: Further Use of Heuristic Methods, Chapter 7 (pp. 199-235) in: Berry, S., Lowndes, V., Trovati, M. (Eds.) Guide to Computational Modelling for Decision Processes: Theory, Algorithms, Techniques and Applications, Springer, 2017 (ISBN 978-973-7677-54-9).

 

Articles:

1.       Alzorba, S., Guenther, C., Popovici, N., Tammer, C., A new algorithm for solving planar multiobjective location problems involving the Manhattan norm, European Journal of Operational Research, Vol. 258 (1) 2017, pp. 35-46.

2.       Bagdasar,O., Popovici, N., Extremal properties of generalized convex vector functions, Journal of Nonlinear and Convex Analysis, accepted August 2015.

3.       Popovici, N., A decomposition approach to vector equilibrium problems, Annals of Operations Research, Vol. 251 (1) (2017), pp. 105-115.

4.       Kuroiwa, D., Popovici, N. Rocca, M.: Characterizations of cone-convex vector-valued functions, Carpathian Journal of Mathematics, Vol. 32 (1) (2016), pp. 79-85.

5.       Kuroiwa, D., Popovici, N., Rocca, M., A characterization of cone-convexity for set-valued functions by cone-quasiconvexity, Set-Valued and Variational Analysis, Vol. 23 (2) (2015), pp. 295-304.

6.       Bagdasar,O., Popovici, N., Local maximum points of explicitly quasiconvex functions, Optimization Letters, Vol. 9 (4) (2015), pp. 769-777.

7.       Alzorba, Sh., Günther, Chr., Popovici, N., A special class of extended multicriteria location problems, Optimization, Vol. 64 (5) (2015), pp. 1305-1320.

8.       Popovici, N., Rocca, M., Scalarization and decomposition of vector variational inequalities governed by bifunctions, Optimization, Vol. 62 (6) (2013), pp. 735-742. 

9.       Popovici, N., Rocca, M., Decomposition of generalized vector variational inequalities, Nonlinear Analysis: Theory, Methods and Applications, Vol. 75 (3) (2012), pp. 1516-1523.

10.    La Torre, D, Popovici, N., Rocca, M., A note on explicitly quasiconvex set-valued maps, Journal of Nonlinear and Convex Analysis, Vol. 12 (1) (2011), pp. 113-118.

11.    La Torre, D., Popovici N., Arcwise cone-quasiconvex multicriteria optimization, Operations Research Letters, Vol. 38 (2) (2010), pp. 143-146.

12.    La Torre, D., Popovici N., Rocca M., Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions, Nonlinear Analysis. Theory, Methods & Applications, Vol. 72 (3-4) (2010), pp. 1909-1915.

13.    Breckner, B. E., Popovici, N., An overview of five separation notions, In: Şt. Cobzaş (ed.): Topics in Mathematics, Computer Science and Philosophy. A Festschrift for Wolfgang W. Breckner on his 65th Anniversary, Presa Universitară Clujeană, Cluj-Napoca, 2008, pp. 43-55.

14.    Popovici, N., Involving the Helly number in Pareto reducibility, Operations Research Letters, Vol. 36 (2008), pp. 173-176.

15.    Popovici, N., Explicitly quasiconvex set-valued optimization, Journal of Global Optimization, Vol. 38 (2007), pp. 103-118.

16.    Ait Mansour, M., Popovici, N., Théra, M., On directed sets and their suprema, Positivity, Vol. 11 (2007), pp. 155-169.

17.    Chiorean, I., Lupşa, L., Popovici, N., Unimodal multicriteria optimization via Fibonacci numbers, Creative Mathematics and Informatics, Vol. 16 (2007), pp. 114-123.

18.    Popovici, N., A note on the boundary of radiant sets, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, Vol. 5 (2007), pp. 119-128.

19.    Popovici, N., Structure of efficient sets in lexicographic quasiconvex multicriteria optimization, Operations Research Letters, Vol. 34 (2006), pp. 142-148.

20.    Lupşa L., Popovici, N., Generalized unimodal multicriteria optimization problems, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 35 (2006),pp.  65-70.

[free full text available at J. Numer. Anal. Approx. Theory]

21.    Popovici, N., Almost explicitly quasiconvex bicriteria optimization, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, Vol. 4 (2006), pp. 101-109.

22.    Popovici, N., Pareto reducible multicriteria optimization problems, Optimization, Vol. 54 (2005), pp. 253-263.

23.    Lupşa L., Popovici, N., A new algorithm for solving multicriteria unimodal optimization problems, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, Vol. 3 (2005), pp. 123-130.

24.    Benoist, J., Popovici, N., Between quasiconvex and convex set-valued maps, Applied Mathematics Letters, Vol. 17 (2004), pp. 245-247.

25.    Benoist, J., Borwein, M. J., Popovici, N., A characterization of quasiconvex vector-valued functions, Proceedings of the American Mathematical Society, Vol. 131 (2003), pp. 1109-1113.

26.    Benoist, J., Popovici, N., Characterizations of convex and quasiconvex set-valued maps, Mathematical Methods of Operations Research, Vol. 57 (2003), pp. 427-435.

27.    Benoist, J., Popovici, N., Generalized convex set-valued maps, Journal of Mathematical Analysis and Applications, Vol. 288 (2003), pp. 161-166.

28.    Popovici, N., A characterization of cone-convex functions, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, Vol. 1 (2003), pp. 123-131.

29.    Benoist, J., Popovici, N., Characterizations of finite dimensional shaded sets, Nonlinear Analysis Forum, Vol. 7 (2002), pp. 67-72.

30.    Popovici, N., Generalized quasiconvex set-valued maps, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 31 (2002), pp. 199-206.

[free full text available at J. Numer. Anal. Approx. Theory]

31.    Popovici, N., (Γ,K)-quasiconvex set-valued maps, In: E. Popoviciu (Ed.), Proceedings of the ''Tiberiu Popoviciu'' Itinerant Seminar of Functional Equations, Approximation and Convexity, Editura SRIMA, Cluj-Napoca, 2002, pp. 223-230.

32.    Popovici, N., Almost Explicitly Quasiconvex Functions, In: E. Popoviciu (Ed.), Séminaire de la théorie de la meilleure approximation, convexité et optimisation, Editura SRIMA, Cluj-Napoca, 2002, pp. 125-133.

33.    Benoist, J., Popovici, N., Contractibility of the efficient frontier of three-dimensional simply-shaded sets, Journal of Optimization Theory and Applications, Vol. 111 (2001), pp. 81-116.

34.    Popovici, N., Scalar characterizations of generalized quasiconvex functions, In: N. Hadjisavvas, J. E. Martinez-Legaz, J.-P. Penot (Eds), Generalized Convexity and Generalized Monotonicity (Proceedings of the 6th International Symposium on Generalized Convexity & Monotonicity, Karlovassi, Samos, Greece, August 30 - September 3, 1999), Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Vol. 502 (2001), pp. 341-348.

35.    Popovici, N., Generalized quasiconvexity via properly characteristic functions associated to binary relations, Acta Mathematica Vietnamica, Vol. 26 (2001), pp. 169-175.

36.    Malivert, C., Popovici, N., The Structure of Efficient Sets in Bicriteria Quasilinear Optimization, Journal of Nonlinear and Convex Analysis, Vol. 2 (2001), pp. 291-304.

37.    Benoist, J., Popovici, N., The structure of the efficient frontier of finite dimensional completely-shaded sets, Journal of Mathematical Analysis and Applications, Vol. 250 (2000), pp. 98-117.

38.    Malivert, C., Popovici, N., Bicriteria linear fractional optimization, In: Nguyen, V. H., Strodiot, J.-J., Tossings, P. (Eds.), Optimization (Proceedings of the 9th Belgian-French-German Conference on Optimization, Namur, Belgium, September 7-11, 1998), Lecture Notes in Economics and Mathematical Systems, Springer, Vol. 481 (2000), pp. 305-319.

39.    Popovici, N., Convexité au sens direct ou inverse et applications dans l'optimisation vectorielle, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 29 (2000), pp. 75-82.

[free full text available at J. Numer. Anal. Approx. Theory]

40.    Popovici, N., Malivert, C., An algorithm for bicriteria optimization involving explicitly quasilinear objective functions, In: G. Wanka (Ed.), Decision Theory and Optimization in Theory and Practice (Proceedings of the 9th Workshop of the GOR Working Group ''Decision Theory and Practice'', Chemnitz, Germany, March 3-5, 1999), Shaker Verlag, Aachen, 2000, pp. 53-62.

41.    Popovici, N., Sur la structure topologique des ensembles d'efficience, Mathematica (Cluj), Vol. 41 (1999), pp. 233-241

42.    Popovici, N., Generalized quasiconvexity with respect to domination-type binary relations, In: L. Lupşa and M. Ivan (Eds.), Analysis, Functional Equations, Approximations and Convexity (Proceedings of the Conference Held in Honour of Professor Elena Popoviciu, Cluj-Napoca, October 15-16, 1999), Carpatica, Cluj-Napoca, 1999, pp. 251-256.

43.    Popovici, N., Polygonal convexity in multicriteria linear fractional optimization, In: E. Popoviciu (Ed.), Research on Theory of Allure, Approximation, Convexity and Optimization, SRIMA, Cluj-Napoca, 1999, pp. 249-256.

44.    Popovici, N., Sur l'approximation des ensembles d'efficience, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 27 (1998), pp. 321-329.

[free full text available at J. Numer. Anal. Approx. Theory]

45.    Popovici, N., On the level sets of (Γ,Ω) -quasiconvex functions, Studia Universitatis Babeş-Bolyai, Ser. Mathematica, Vol. 43 (1998), pp. 71-78.

46.    Popovici, N., Sur une notion abstraite de quasiconvexité, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 26 (1997), pp. 191-196.

[free full text available at J. Numer. Anal. Approx. Theory]

47.    Popovici, N., Multicriteria optimization with unimodal objective functions, In: D.D. Stancu, Gh. Coman, W.W.Breckner and P. Blaga (Eds.), Approximation and Optimization, Vol. I (Proceedings of the International Conference on Approximation and Optimization, Cluj-Napoca, July 29 - August 1, 1996), Transilvania Press, Cluj-Napoca, 1997, pp. 341-344.

48.    Popovici, N., The excess from efficiency in vector optimization, In: A. Göpfert, J. Seeländer and Chr. Tammer (Eds.), Methods of Multicriteria Decision Theory (Proceedings of the 6th Workshop of the DGOR-Working Group Multicriteria Optimization and Decision Theory, Alexisbad, Germany, March 11-14, 1996), Hänsel-Höhenhausen Verlag, Egelsbach, 1997, pp. 63-67.

49.    Popovici, N., L'écart d'efficience dans l'optimisation vectorielle, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 25 (1996), pp. 217-224.

[free full text available at J. Numer. Anal. Approx. Theory]

50.    Popovici, N., Convexité en espaces métriques via l'efficience de Pareto, Mathematica (Cluj), Vol. 38 (1996), pp. 169-175.

51.    Popovici, N., Suites efficientes dans l'optimisation vectorielle, Babeş-Bolyai University, Faculty of Mathematics, Research Seminars, Seminar on Mathematical Analysis, Preprint Nr. 7 (1994), pp. 95-105.

52.    Popovici, N., On a special class of Pareto bicriterial optimization problems, Revue d'Analyse Numérique et de Théorie de l'Approximation, Vol. 19 (1990), pp. 163-168

[free full text available at J. Numer. Anal. Approx. Theory]

53.    Popovici, N., The degree of efficiency in the multiobjective optimization problems, Babeş-Bolyai University, Faculty of Mathematics and Informatics, Research Seminars, Seminar on Mathematical Analysis, Preprint No. 7 (1990), pp. 143-154.

 

Editorial materials

 

54.    Mordukhovich, B.S., Popovici, N., Sheu, R.-L., Preface: special issue of JOGO-GCM10. J. Global Optim., Vol. 57 (3) (2013), pp. 613-615.

 

Citations

 

       1.  The article [Alzorba, S., Guenther, C., Popovici, N., Tammer, C., A new algorithm for solving planar multiobjective location problems involving the Manhattan norm, European Journal of Operational Research, Vol. 258 (1) 2017, pp. 35-46] cited in:

·      C. Bosch, C.L. García, T. Gilsdorf, C. Gómez-Wulschner, R. Vera: Fixed points of set-valued maps in locally complete spaces, Fixed Point Theory and Applications, 2017:13.

 

       2.  The article [Popovici, N., Rocca, M., Scalarization and decomposition of vector variational inequalities governed by bifunctions, Optimization, Vol. 62 (6) (2013), pp. 735-742] cited in:

·      A.A. Khan, Chr. Tammer, C. Zălinescu, Set-valued optimization. An introduction with applications, Springer, Berlin, 2015.

 

       3.  The article [La Torre, D, Popovici, N., Rocca, M., A note on explicitly quasiconvex set-valued maps, Journal of Nonlinear and Convex Analysis, Vol. 12 (1) (2011), pp. 113-118] cited in:

·     C. Gutiérrez, V. Novo, J. L. Ródenas-Pedregosa, T. Tanaka: Nonconvex separation functional in linear spaces with applications to vector equilibria, SIAM J. Optim., 26 (4) (2016), 2677-2695.

 

       4.  The article [La Torre, D., Popovici N., Arcwise cone-quasiconvex multicriteria optimization, Operations Research Letters, Vol. 38 (2) (2010), pp. 143-146] cited in:

·     N. Hamada: Simple Problems. The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts, arXiv:1709.10377v1

·     GuoLin Yu: Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization, Journal of Inequalities and Applications, 2015, 2015:317

 

       5.  The article [LaTorre D., Popovici N., Rocca M.: Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions, Nonlinear Analysis. Theory, Methods & Applications, 72 (3-4) (2010), 1909-1915] cited in:

·     C. Gutiérrez, V. Novo, J. L. Ródenas-Pedregosa, T. Tanaka: Nonconvex separation functional in linear spaces with applications to vector equilibria, SIAM J. Optim., 26 (4) (2016), 2677-2695.

·     S. Khoshkhabar-amiranloo, E. Khorram, M. Soleimani-damaneh: Nonlinear scalarization functions and polar cone in set optimization, Optimization Letters, 11 (2017) (3), 521–535

·     GuoLin Yu: Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization, Journal of Inequalities and Applications, 2015, 2015:317

·     E. Kiyani, M. Soleimani-Damaneh: Approximate proper efficiency on real linear vector spaces, Pacific Journal of Optimization, 10 (4) (2014), 715-734

·     I. Kuwano: Some minimax theorems of set-valued maps and their applications, Nonlinear Analysis: Theory, Methods & Applications, 109 (2014), 85–102.

·     S. Khoshkhabar-amiranloo, M. Soleimani-damaneh: Scalarization of set-valued optimization problems and variational inequalities in topological vector spaces, Nonlinear Analysis. Theory, Methods & Applications, 75 (2012) 1429–1440.

 

       6.  The article [Popovici, N., Involving the Helly number in Pareto reducibility, Operations Research Letters, Vol. 36 (2008), 173-176] cited in:

·     C. Gunther, C. Tammer: On generalized-convex constrained multi-objective optimization, Martin-Luther-Universitat Halle-Wittenberg, Institut fur Mathematik, Report No. 02 (2017).

·     P. G. Georgiev, D. T. Luc, P. M. Pardalos: Robust aspects of solutions in deterministic multiple objective linear programming, European Journal of Operational Research, 229 (2013), 29-36.

 

       7.  The preprint [La Torre, D., Popovici, N., Rocca, M.: Scalar characterization of explicitly quaxiconvex set-valued maps, http://wp.demm.unimi.it/tl files/wp/2008/DEMM-2008 001wp.pdf (2008)] cited in:

·     C. Gutiérrez, V. Novo, J. L. Ródenas-Pedregosa, T. Tanaka: Nonconvex separation functional in linear spaces with applications to vector equilibria, SIAM J. Optim., 26 (4) (2016), 2677-2695.

 

       8.  The article [Popovici, N.: Explicitly quasiconvex set-valued optimization, Journal of Global Optimization 38 (2007), 103-118] cited in:

·     N. Hamada: Simple Problems. The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts, arXiv:1709.10377v1

·     F. Li, X.M. Yang: Characterizations of properly quasiconvex set-valued maps, Journal of Nonlinear and Convex Analysis, 18 (2017) (3), 473-483.

·     A. Mohammadi, M. Soleimani-damaneh: Reconstruction of the core convex topology and its applications in vector optimization and convex analysis, arXiv:1704.06932

·     C. Gutiérrez, V. Novo, J. L. Ródenas-Pedregosa, T. Tanaka: Nonconvex separation functional in linear spaces with applications to vector equilibria, SIAM J. Optim., 26 (4) (2016), 2677-2695.

·     GuoLin Yu: Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization, Journal of Inequalities and Applications, 2015, 2015:317

·     I. Kuwano, T. Tanaka: Continuity of cone-convex functions, Optimization Letters 6 (2012) (8), 1847-1853.

·     Sh. Alzorba, Chr. Guenther, Algorithms for Multicriteria Location Problems, In: T.E. Simos, G.Psihoyios, C. Tsitouras et al. (Eds.), International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Kos, Greece, Sep 19-25, 2012, Numerical Analysis and Applied Mathematics (ICNAAM 2012), Vols. A and B, Book Series: AIP Conference Proceedings, Vol. 1479, 2286-2289, 2012.

·     Chai, Yan-Fei; Cho, Yeol Je; Li, Jun: Some characterizations of ideal points in vector optimization problems. Journal of Inequalities and Applications, Volume 2008 (2008), Art. ID 231845, 8 pp.

 

       9.  The article [Ait Mansour, M., Popovici, N., Théra, M., On directed sets and their suprema, Positivity, Vol. 11 (2007), pp. 155-169] cited in:

·     M. Ait Mansour and H. Riahi: On the cone minima and maxima of directed convex free disposal subsets and applications, Minimax Theory and its Applications, 1 (2016) (2), 163-195.

 

       10.  The article [Popovici, N.: Structure of efficient sets in lexicographic quasiconvex multicriteria optimization, Operations Research Letters, 34 (2) (2006), 142-148] cited in:

·     N. Hamada: Simple Problems. The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts, arXiv:1709.10377v1

·     C. Gunther, C. Tammer: On generalized-convex constrained multi-objective optimization, Martin-Luther-Universitat Halle-Wittenberg, Institut fur Mathematik, Report No. 02 (2017).

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·     M. Gardenghi, M. Wiecek Algebra of Efficient Sets For Complex Systems, Clemson University, Department of Mathematical Sciences, Technical Report TR2009_4_GW, 2009.

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       12.  The article [Benoist, J., Borwein, M. J., Popovici, N.: A characterization of quasiconvex vector-valued functions, Proceedings of the American Mathematical Society, 131 (2003), 1109-1113] cited in:

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·     E. Ernst, A. Zaffaroni: Characterizing Sets of Lower Bounds: a Hidden Convexity Result, Set-Valued and Variational Analysis, Online 2017, doi:10.1007/s11228-017-0416-9

·     Phan Nhat Tinh: Characterizations of generalized convex functions in terms of coderivative, Hue University Journal of Science, 116 (2016) (2), 91-101.

·     Tran Ngoc Thang, Dinh The Luc, Nguyen Thi Bach Kim: Solving generalized convex multiobjective programming problems by a normal direction method, Optimization, 65 (2016) (12), 2269-2292.

·     GuoLin Yu: Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization, Journal of Inequalities and Applications, 2015, 2015:317.

·     M. Ait Mansour and H. Riahi: On the cone minima and maxima of directed convex free disposal subsets and applications, Minimax Theory and its Applications, 1 (2016) (2), 163-195.

·     M. Chinaie, J. Zafarani: A new approach to constrained optimization via image space analysis, Positivity, 20 (2016) (1), 99-114.

·     G. P. Crespi, A. H. Hamel, C. Schrage:  A Minty variational principle for set optimization, Journal of Mathematical Analysis and Applications, 423 (2015)(1), 770-796.

·     S. Drapeau, A. H. Hamel, M. Kupper: Complete duality for quasiconvex and convex set-valued functions, Set-Valued and Variational Analysis, 24 (2016) (2), 253-275.

·     S. Suneja, M. Sharma: ε-Optimality in Multivalued Optimization, American Journal of Operations Research, 3 (2013) (4), 413-420.

·     J. Y. Bello Cruz, G. C. Bento, G. Bouza Allende, R. F. B. Costa: The inexact projected gradient method for quasiconvex vector functions, arXiv:1212.1048v1

·     M. Soleimani-damaneh: Characterizations and applications of generalized invexity and monotonicity in Asplund spaces, TOP 20 (2012) (3), 592-613.

·     S. Suzuki: Observations of constraint qualifications for quasiconvex programming, Proceedings of the 3th Asian Conference on Nonlinear Analysis and Optimization, Matsue, Japan, 2012, 303-313.

·     S. Suzuki, D. Kuroiwa: Some constraint qualifications for quasiconvex vector-valued systems, Journal of Global Optimization, 55 (2013) (3), 539-548.

·     F. Flores-Bazan, E. Hernandez: Optimality conditions for a unified vector optimization problem with not necessarily preordering relations, Journal of Global Optimization 56 (2013) (2), 299-315.

·     F. Flores-Bazan, F. Lara: Inner and outer estimates for solution sets and their asymptotic cones in vector optimization, Optimization Letters, 6 (2012) (7), 1233-1249.

·     M. Chinaie, J. Zafarani: Image space analysis and scalarization for ε-optimization of multifunctions, Journal of Optimization Theory and Applications, 157 (2013) (3), 685-695.

·     J.Y. Bello Cruz, L.R. Lucambio Pérez, J.G. Melo: Convergence of the projected gradient method for quasiconvex multiobjective optimization, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 5268-5273.

·     L. Nascimento, G. Riella: A class of incomplete and ambiguity averse preferences, Journal of Economic Theory, 146 (2011), 728-750.

·     M. Soleimani-damaneh: E-convexity and its generalizations, International Journal of Computer Mathematics, 88 (2011), 3335-3349.

·     J. Fu, S. Wang: Symmetric vector quasi-equilibrium problems for set-valued mappings, Acta Math. Appl. Sin. 34 (2011) (1), 40-49.

·     G. P. Crespi, I. Ginchev, M. Rocca: Minty variational principle for set-valued variational inequalities. Pacific Journal of Optimization, 6 (2010), 39-56.

·     M. Chinaie, J. Zafarani: Image space analysis and scalarization of multivalued optimization, Journal of Optimization Theory and Applications, 142 (2009), 451-467.

·     M. Soleimani-damaneh: On generalized convexity in Asplund spaces, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 3072-3075.

·     F. Flores-Bazan, C. Vera: Unifying efficiency and weak efficiency in generalized quasiconvex vector minimization on the real-line, International Journal of Optimization: Theory, Methods and Applications, 1 (2009) (3), 247-265.

·     T. Jabarootian, J. Zafarani: Characterizations of preinvex and prequasiinvex set-valued maps, Taiwanese Journal of Mathematics, 13 (2009) (3), 871-898.

·     I. Ginchev: Vector optimization problems with quasiconvex constraints, Journal of Global Optimization, 44 (2009), 111-130.

·     G. P. Crespi, I. Ginchev, M. Rocca: Some remarks on the Minty vector variational principle, Journal of Mathematical Analysis and Applications, 345 (2008), 165–175.

·     Dinh The Luc: Pareto Optimality, In: A. Chinchuluun, P. M. Pardalos, A. Migdalas, L. Pitsoulis (Eds.), Pareto Optimality, Game Theory and Equilibria, Springer Optimization and its Applications, 17, Springer, 2008, 481-516.

·     M. Soleimani-damaneh: Characterization of nonsmooth quasiconvex and pseudoconvex functions, Journal of Mathematical Analysis and Applications 330 (2007), 1387-1392.

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·     G. P . Crespi, I. Ginchev, M. Rocca: Points of Efficiency in Vector Optimization with Increasing-along-rays Property and Minty Variational Inequalities, In: I. V. Konnov, D. T. Luc, A. M. Rubinov (Eds.), Generalized Convexity and Related Topics, Lecture Notes in Economics and Mathematical Systems 583, Springer, Berlin Heidelberg, 2006, 209-226.

·     J. Gwinner: On the Work of W. Oettli in Generalized Convexity and Nonconvex Optimization - a Review and Some Perspectives, In: I. V. Konnov, D. T. Luc, A. M. Rubinov (Eds.), Generalized Convexity and Related Topics, Lecture Notes in Economics and Mathematical Systems 583, Springer, Berlin Heidelberg, 2006, 297-314.

·     D. T. Luc: Generalized convexity in vector optimization, Chapter in: N. Hadjisavvas, S. Komlósi, S. Schaible (Eds.), Handbook of generalized convexity and generalized monotonicity, Nonconvex Optimization and its Applications 76,  Springer, New York, 2005, 195-236.

 

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·     M. Soleimani-damaneh: Characterizations and applications of generalized invexity and monotonicity in Asplund spaces, TOP 20 (2012) (3), 592-613.

·     Hu-Nan Li, Yu-Lan Liu: Cone Quasi-convexity of Set-Valued Mappings in Topological Vector Spaces, The Ninth International Symposium on Operations Research and Its Applications (ISORA’10), Chengdu-Jiuzhaigou, China, August 19–23, 2010, ORSC & APORC, pp. 83–88.

·     M. Soleimani-damaneh: On generalized convexity in Asplund spaces, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 3072-3075.

·     Ya-Ping Fang, Nan-Jing Huang: Conditions for the Equivalence of Cone Preinvexity and Cone Weak Preinvexity of Set-Valued Mappings, Sichuan University, China, 2008.

·     M. Soleimani-damaneh: Characterization of nonsmooth quasiconvex and pseudoconvex functions, Journal of Mathematical Analysis and Applications 330 (2007), 1387-1392.

 

       14. The article [Benoist, J., Popovici, N.: Characterizations of convex and quasiconvex set-valued maps, Mathematical Methods of Operations Research 57 (2003), 427-435] cited in:

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·     F. Li, X.M. Yang: Characterizations of properly quasiconvex set-valued maps, Journal of Nonlinear and Convex Analysis, 18 (2017) (3), 473-483.

·     G. Eichfelder, C. Krüger, A. Schöbel: Decision uncertainty in multiobjective optimization, Journal of Global Optimization, Online 2017, doi:10.1007/s10898-017-0518-9

·     Fei Li, Liping Tang, Xinmin Yang: A kind of cone-convexity for set-valued maps and its scalarization, Operations Research Transactions, 20 (2016) (4), 21-29

·     GuoLin Yu: Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization, Journal of Inequalities and Applications, 2015, 2015:317

·     M. Chinaie, J. Zafarani: A new approach to constrained optimization via image space analysis, Positivity, published online 29 May 2015, DOI 10.1007/s11117-015-0343-7

·     G. P. Crespi, D. Kuroiwa, M. Rocca: Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization, Annals of Operations Research, Online 21 Feb 2015, DOI: 10.1007/s10479-015-1813-9

·     G. P. Crespi, A. H. Hamel, C. Schrage:  A Minty variational principle for set optimization, Journal of Mathematical Analysis and Applications, 423 (2015)(1), 770-796.

·     A. H. Hamel, F. Heyde, A. Löhne, B. Rudloff, C. Schrage: Set optimization - a rather short introduction, arXiv:1404.5928v2

·     S. Drapeau, A. H. Hamel, M. Kupper: Complete duality for quasiconvex and convex set-valued functions, Set-Valued and Variational Analysis, published online 29 May 2015, DOI 10.1007/s11228-015-0332-9

·     G. P. Crespi, D. Kuroiwa, M. Rocca: Convexity and global well-posedness in set-optimization, Taiwanese Journal of Mathematics, 18 (6) (2014), 1897-1908

·     G. Eichfelder: Variable Ordering Structures in Vector Optimization, Springer, 2014.

·     Tinh, Phan, Kim, Do: On generalized Fenchel-Moreau theorem and second-order characterization for convex vector functions, Fixed Point Theory and Applications 2013:328 (2013).

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·     X. X. Huang, J. C. Yao: Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems, Journal of Global Optimization, 55 (2013) (3), 611-626

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·     J. Fu, S. Wang: Symmetric vector quasi-equilibrium problems for set-valued mappings, Acta Math. Appl. Sin. 34 (2011) (1), 40-49.

·     G. P. Crespi, I. Ginchev, M. Rocca: Minty variational principle for set-valued variational inequalities. Pacific Journal of Optimization, 6 (2010), 39-56.

·     M. Chinaie, J. Zafarani: Image space analysis and scalarization of multivalued optimization, Journal of Optimization Theory and Applications, 142 (2009), 451-467.

·     T. Jabarootian, J. Zafarani: Characterizations of preinvex and prequasiinvex set-valued maps, Taiwanese Journal of Mathematics, 13 (2009) (3), 871-898.

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·        H. Leiva, N. Merentes, K. Nikodem, J. L. Sánchez: Strongly convex set-valued maps, Journal of Global Optimization, DOI 10.1007/s10898-013-0051-4, OnlineFirst 2013.

·        M. Oveisiha, J. Zafarani: Super efficient solutions for set-valued maps, Optimization  62 (2013) (6), 817-834.

·        T. Jabarootian, J. Zafarani: Characterizations of preinvex and prequasiinvex set-valued maps, Taiwanese Journal of Mathematics, 13 (2009) (3), 871-898.

 

16. The article [Benoist, J., Popovici, N.: Characterizations of finite dimensional shaded sets, Nonlinear Analysis Forum 7 (2002), 67-72] cited in:

·     D. Duca: Multicriteria optimization in complex space, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.

      

      17. The article [Benoist, J., Popovici, N.: Contractibility of the efficient frontier of three-dimensional simply-shaded sets, Journal of Optimization Theory and Applications 111 (2001), 81-116] cited in:

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·     N. Q. Huy, N. D. Yen: Contractibility of the solution sets in strictly quasiconcave vector maximization on noncompact domains, Journal of Optimization Theory and Applications 124 (2005), no. 3, 615-635.

·     D. T. Luc: Generalized convexity in vector optimization, Chapter in: N. Hadjisavvas, S. Komlósi, S. Schaible (Eds.), Handbook of generalized convexity and generalized monotonicity, Nonconvex Optimization and its Applications 76,  Springer, New York, 2005, 195-236.

·     A. Daniilidis, Y. Garcia Ramos: Some remarks on the class of continuous (semi-)strictly quasiconvex functions, Journal of Optimization Theory and Applications, 133 (2007), 37-48.

·     D. Duca: Multicriteria optimization in complex space, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.

      

       18. The article [Malivert, C., Popovici, N.: The structure of efficient sets in bicriteria quasilinear optimization, Journal of Nonlinear and Convex Analysis 2 (2001), 291-304] cited in:

·     A. Engau: Nonlinear multiobjective programming, in: J. J. Cochran (Ed.), Wiley Encyclopedia of Operations Research and Management Science, John Wiley & Sons, 2010.

·     D. Duca: Multicriteria optimization in complex space, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.

      

       19. The article [Benoist, J., Popovici, N.: The structure of the efficient frontier of finite dimensional completely-shaded sets, Journal of Mathematical Analysis and Applications 250 (2000), 98-117] cited in:

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·     Z. D. Slavov: On Pareto sets in multi-criteria optimization, Union of Bulgarian Mathematicians, Vol. 40, No 1, (2011), 207-212.

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·     E. Miglierina, E. Molho, F. Patrone, S. H. Tijs: Axiomatic approach to approximate solutions in multiobjective optimization, Decisions in Economics and Finance 31 (2008), 95–115.

·     N. Q. Huy, N. D. Yen: Contractibility of the solution sets in strictly quasiconcave vector maximization on noncompact domains, Journal of Optimization Theory and Applications 124 (2005), no. 3, 615-635.

·     D. Duca: Multicriteria optimization in complex space, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.

·     N. Q. Huy: Topology of the efficient sets of convex sets in R2, Vietnam Journal of Mathematics 31 (2003) (1), 45-55.

·     N. Q. Huy: Arcwise connectedness of the solution sets of a semistrictly quasiconcave vector maximization problem, Acta Mathematica Vietnamica 27 (2002) (2), 165-174.

      

       20. The article [Malivert, C., Popovici, N.: Bicriteria linear fractional optimization, In: Nguyen, V. H., Strodiot, J.-J., Tossings, P. (Eds.), Optimization. Proceedings of the 9th Belgian-French-German Conference on Optimization, Namur, Belgium, September 7-11, 1998. Lecture Notes in Economics and Mathematical Systems 481, Springer Verlag, 2000, 305-319] cited in:

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·     T. N. Hoa, T. D. Phuong, N. D. Yen: Bicriteria strictly quasiconcave maximization on noncompact sets, Nonlinear Analysis Forum 10 (2005) (2), 137-144.

·     G. M. Lee, N. N. Tam, N. D. Yen:  Quadratic programming and affine variational inequalities. A qualitative study, Nonconvex Optimization and Its Applications 78, Springer Netherlands, 2005, 143-154.

·     T. N. Hoa, T. D. Phuong, N. D. Yen: Number of connected components of the solution sets in linear fractional vector optimization, Vietnamese Academy of Science and Technology, Institute of Mathematics, Preprint Series 11/2002.

      

       21. The article [Popovici, N.: Polygonal convexity in multicriteria linear fractional optimization, In: E. Popoviciu (Ed.), Research on Theory of Allure, Approximation, Convexity and Optimization, SRIMA, Cluj-Napoca, 1999, 249-256] cited in:

·     I. M. Stancu-Minasian: A sixth bibliography of fractional programming, Optimization 55 (2006) (4), 405-428.

      

       22. The article [Popovici, N.: Sur l'approximation des ensembles d'efficience, Revue d'Analyse Numérique et de Théorie de l'Approximation 27 (1998), 321-329] cited in:

·     S. Ruzika, M. M. Wiecek: Approximation methods in multiobjective programming, Journal of Optimization Theory and Applications 126 (2005) (3), 473-501.

      

       23. The article [Popovici, N.: Sur une notion abstraite de quasiconvexité, Revue d'Analyse Numérique et de Théorie de l'Approximation 26 (1997), 191-196] cited in:

·     C. Malivert, N. Boissard: Structure of efficient sets for strictly quasi-convex objectives, Journal of Convex Analysis  1  (1994)  (2), 143-150 (articolul este citat ca preprint Sur une notion de quasi-convexite pour des fonctions vectorielles).

      

       24. The article [Popovici, N.: On a special class of Pareto bicriterial optimization problems, Revue d'Analyse Numérique et de Théorie de l'Approximation 19 (1990), 163-168] cited in :

·     A. Cambini, L. Martein, I. M. Stancu-Minasian: A survey of bicriteria fractional problems, Advanced Modeling and Optimization 1 (1999) (1), 9-46.

      

       25. The Ph.D. thesis [Popovici, N.: Contribution à l’optimisation vectorielle, Université de Limoges, 1995] cited in:

·     D. T. Luc: Pareto Optimality, In: A. Chinchuluun, P. M. Pardalos, A. Migdalas, L. Pitsoulis (Eds.), Pareto Optimality, Game Theory and Equilibria, Springer Optimization and its Applications 17, Springer, 2008, 481-516.

·     D. T. Luc: Generalized convexity in vector optimization, In: N. Hadjisavvas, S. Komlósi, S. Schaible (Eds.), Handbook of generalized convexity and generalized monotonicity, Nonconvex Optimization and its Applications 76,  Springer, New York, 2005, 195-236.

·     G. Isac, V. A. Bulavsky, V. V. Kalashnikov: Complementarity, Equilibrium, Efficiency and Economics. Nonconvex Optimization and its Applications, 63. Kluwer Academic Publishers, Dordrecht, 2002.

·     N. Hadjisavvas: Generalized convexity, generalized monotonicity and nonsmooth analysis, Chapter in: N. Hadjisavvas, S. Komlósi, S. Schaible (Eds.), Handbook of generalized convexity and generalized monotonicity, Nonconvex Optimization and its Applications 76,  Springer, New York, 2005, 465-499.

·     J. Benoist: Connectedness of the efficient set for strictly quasiconcave sets, Journal of Optimization Theory and Applications 96 (1998) (3), 627-654.

      

       26. The book [Breckner, B. E., Popovici, N.: Convexity and Optimization: An Introduction, EFES, Cluj-Napoca, 2006] cited in:

·     W. W. Breckner, T. Trif: Convex Functions and Related Functional Equations. Selected Topics. Presa Universitară Clujeană, 2008.

 

 

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