Optimization and dynamical systems: geometric and logic-based techniques

Project code: PN-III-P1-1.1-TE-2019-1306

Period: November 2020 - October 2022

Host: Babeş-Bolyai University

Research team: Adriana Nicolae (principal investigator), Adriana Buică, Adrian Viorel, Mihai-Radu Truşcă

Abstract: This project deals with problems in (convex and nonconvex) optimization and in dynamical systems relying on geometric-analytic tools and techniques suited with the structure of the spaces under consideration. In part, ideas stemming from an applied subfield of logic, called proof-mining, will also be used. More precisely, we will address specific algorithms in geodesic metric spaces of bounded curvature in the sense of Alexandrov, but will focus as well on other more subtle constructions and results with important applications in optimization theory, among others. In addition, we will apply proof mining techniques to obtain effective results for algorithms considering the context as general as possible. Besides, we will study other interesting properties in optimization and dynamical systems, including the finite length and periodicity of solutions of differential equations.

Summary: In this project we addressed research directions corresponding to the two parts of the project:
  1. Optimization in Alexandrov spaces.
  2. Asymptotic behavior of nonlinear algorithms and continuous dynamical system.
The obtained results fit within the following main objectives of the project: We highlight below some ideas from each stage of the project: In short, this project addressed theoretical aspects of optimization and dynamical systems using techniques from different areas which resulted in an interdisciplinary approach to the considered problems.

Publications: Work in progress: Other research papers are close to completion. Details will be added once they are submitted for publication.

Conference talks: Seminar talks: