Exploratory
Research Project PN2-IDEI-PCE-2008-2, Code CNCSIS 2261, Contract No. 543
Project
duration: 3 years (2009, 2010, 2011)
ADVANCED RESEARCHES ON
VECTOR AND SET-VALUED OPTIMIZATION PROBLEMS, AND VARIATIONAL INEQUALITIES,
UNDER GENERALIZED CONVEXITY ASSUMPTIONS
Project
manager: Assoc. prof. Nicolae Popovici, Ph.D.
Assoc. prof. Nicolae POPOVICI,
Ph.D. -
project manager
Prof. Wolfgang Werner BRECKNER,
Ph.D.
VECTOR AND SET-VALUED OPTIMIZATION, VARIATIONAL
INEQUALITIES HAVE ENCOUNTERED A DYNAMIC DEVELOPMENT OFFERING A FRUCTUOUS
FRAMEWORK FOR THE APPLICABILITY OF ADVANCED THEORETICAL ACQUISITIONS FROM
CONVEX, NONLINEAR AND SET-VALUED ANALYSIS.
FROM SOME RECENT THEORETICAL OPEN PROBLEMS,
CONSIDERING THEIR PRACTICAL APPLICABILITY, TWELVE OBJECTIVES ARE PROPOSED:
-
STUDY OF THE PARETO REDUCIBILITY FOR MULTICRITERIA
OPTIMIZATION PROBLEMS WHOSE OBJECTIVE FUNCTIONS ARE DEFINED ON ARCWISE
CONNECTED DOMAINS;
-
DEVELOPMENT OF SOME SEQUENTIAL OPTIMALITY
CONDITIONS;
-
EXTENSION OF SOME RECENT RESULTS WITH RESPECT TO THE
WELL-POSED VECTOR OPTIMIZATION PROBLEMS UNDER GENERALIZED CONVEXITY;
-
INTRODUCTION OF AN APPROPRIATE REDUCIBILITY RESULT FOR
VECTOR VARIATIONAL INEQUALITIES;
-
STUDY OF SET-VALUED DUALITY CONCEPTS;
-
SYSTEMATIZATION OF GENERALIZED CONVEXITY CONCEPTS
FOR FUNCTIONS WITH VALUES IN VECTOR TOPOLOGICAL ORDERED SPACES;
-
DEVELOPMENT OF A SOLUTION METHOD FOR VARIATIONAL
INEQUALITIES GOVERNED BY GENERALIZED MONOTONE OPERATORS;
-
EXTENSION OF THE WELL-POSEDNESS CONCEPT TO
SET-VALUED OPTIMIZATION;
-
INTRODUCTION OF GENERALIZED PARETO REDUCIBILITY FOR
VECTOR OPTIMIZATION PROBLEMS THROUGH EXTREMAL SUBSETS OF THE ORDER CONE;
-
STUDY OF THE TOPOLOGICAL STRUCTURE OF THE EFFICIENT
SOLUTIONS SET IN VECTOR OPTIMIZATION PROBLEMS;
-
EXTENSION OF SOME REMARKABLE RESULTS WITH RESPECT TO
OPTIMIZATION PROBLEMS TO LINEAR SPACES WITH ASYMMETRIC NORM;
-
OBTAINMENT OF LAGRANGE MULTIPLIER RULES IN
SET-VALUED OPTIMIZATION USING DERIVED SETS. THE RESEARCH RELIES ON ARTICLES BY
PROJECT MEMBERS.
1.
Davide LA TORRE, Nicolae POPOVICI: Arcwise
cone-quasiconvex multicriteria optimization, Operations Research Letters,
Vol. 38 (2), 2010, 143-146,
[ISI 2008 Impact factor: 0.830; ISI 2009 Impact factor: 0.681]
2.
Anca GRAD: Improved sequential optimality conditions
for vector optimization problems with cone-epi-closed
functions, Annals
of the Tiberiu Popoviciu
Seminar of Functional Equations, Approximation and Convexity, Vol. 7, 2009,
55-72.
3.
Monica BIANCHI,
Gabor KASSAY, Rita PINI: Well-posedness for
vector equilibrium problems, Mathematical Methods of
Operations Research, Vol. 70 (1), 2009, 171-182 [ISI 2008 Impact factor: 0.476; ISI 2009 Impact factor: 0.522]
4.
Nicolae POPOVICI, Matteo ROCCA: Pareto
reducibility of vector variational inequalities, Quaderni di Ricerca,
Universita dell'Insubria, Dipartimento di Economia, 2010/4
5.
Anca GRAD: Quasi-relative interior-type constraint
qualifications ensuring strong Lagrange duality for optimization problems with
cone and affine constraints, Journal of Mathematical
Analysis and Applications, Vol. 361 (1), 2010, 86-95, [ISI 2008 Impact
factor: 1.046;
ISI 2009 Impact factor: 1.225]
6.
Davide LA TORRE,
Nicolae POPOVICI, Matteo ROCCA: Scalar
characterizations of weakly cone-convex and weakly cone-quasiconvex functions,
Nonlinear Analysis:
Theory, Methods & Applications, Vol. 72 (3-4), 2010, 1909-1915 [ISI
2008 Impact factor: 1.295;
ISI 2009 Impact factor: 1.487]
7.
Anca GRAD: Converse duality for a new Fenchel dual problem in finite dimensional vector
optimization, Annals
of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and
Convexity, Vol. 8, 2010, 27-37.
8.
Adela CAPATA, Gabor KASSAY, Boglarka
MOSONI: On weak multifunctions
equilibrium problems, In: Burachik, Regina S.;
Yao, Jen-Chih (Eds.), Variational
Analysis and Generalized Differentiation in Optimization and Control. In Honor
of Boris S. Mordukhovich, Springer
Series in Optimization and its
Applications, Vol. 47, 2010, 133-148.
9.
Giancarlo BIGI,
Adela CAPATA, Gabor KASSAY: Existence
results for strong vector equilibrium problems and their applications, Optimization,
DOI:
10.1080/02331934.2010.528761, [ISI 2009 Impact factor: 0.616]
10.
Davide LA TORRE,
Nicolae POPOVICI, Matteo ROCCA: A note on
explicitly quasiconvex set-valued maps, Journal of
Nonlinear and Convex Analysis, Vol.12 (1) (2011), 113-118. [ISI 2009 Impact
factor: 0.585]
11.
Stefan COBZAS: Completeness
in quasi-metric spaces and Ekeland variational principle, Topology and its
Applications, Vol.158 (8), 2011, 1073-1084. [ISI 2009 Impact factor: 0.441]
12.
Nicolae POPOVICI, Matteo ROCCA: Decomposition
of vector variational inequalities, Nonlinear
Analysis: Theory, Methods and Applications, Vol.75 (3), 2012, 1516-1523 [ISI 2009 Impact factor: 1.487, ISI 2010 Impact factor:
1.279]
13.
Anca GRAD: Generalized duality and optimality
conditions, Editura Mega, Cluj-Napoca, 2010 (210
pp., ISBN 978-606-543-098-3)
14.
Anca GRAD: Quasi interior-type optimality conditions in
set-valued duality, Journal of Nonlinear and Convex Analysis, in press [ISI
2010 Impact factor: 0,738]
15.
Monica BIANCHI, Gabor KASSAY, Rita PINI: Conditioning for optimization problems under
general perturbations, Nonlinear
Analysis: Theory, Methods and Applications, Vol. 75 (1) (2012), 37-45 [ISI
2010 Impact factor: 1.279]
16.
Gabor KASSAY, Simeon REICH, Shoham
SABACH: Iterative methods for solving
systems of variational inequalities in reflexive Banach spaces, SIAM
Journal on Optimization, Vol. 21 (4) (2011), 1319-1344 [ISI 2010 Impact
factor: 2,079]
17.
Nicolae POPOVICI, Matteo ROCCA: Scalarization and
decomposition of vector variational inequalities
governed by bifunctions, Optimization,
DOI:10.1080/02331934.2012.672984, [ISI 2010 Impact factor: 0,509]
18.
Stefan COBZAS: Ekeland variational principle in asymmetric locally
convex spaces, Topology
and its Applications, DOI: 10.1016/j.topol.2012.04.015, [ISI 2010 Impact
factor: 0.447]
19.
Stefan COBZAS: Functional
analysis in asymmetric normed spaces, submitted to
Quaderni di Matematica, Caserta, Seconda Universita di Napoli
20.
Anca GRAD: Generalized interior characterizations for
saddle points, Annals
of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and
Convexity, Vol. 9 (2011), 47-57
21.
Stefan COBZAS: Functional
Analysis in Asymmetric Normed Spaces, Birkhauser Mathematics Series: Frontiers in Mathematics,
Springer Basel (ISBN 978-3-0348-0477-6)
22.
Wolfgang W.
BRECKNER, Rational s-Convexity. A
Generalized Jensen-Convexity, Presa Universitara Clujeana,
Cluj-Napoca, 2011 (165 pp., ISBN: 978-973-595-325-6)
23.
Gabor KASSAY: The
equilibrium problem and its applications to optimization, minimax
problems, and Nash equilibria, Chapter 8 in: Q.
H. Ansari (Ed.), Topics
in Nonlinear Analysis and Optimization, World Education, Delhi, 2012, pp.
203-226, ISBN 978-81-909873-3-2