EXPLORATORY RESEARCH PROJECT PN-III-P4-ID-PCE-2016-0188, nr. 10/2017
Director: Prof. dr. Constantin ZALINESCU
1. PROPOSAL'S TITLE
Proposal's Title: Variational approaches to set-valued optimization and applications
1.1 Thematic fields :
- 11 Main Sciences: Mathematics
The research grant application we propose aims a thorough study of set-valued vector optimization problems, a topic which is at the confluence of the areas of nonlinear variational analysis and optimization theory. Both the multitude of applications in various fields (including economic sciences, artificial intelligence, behavioral sciences), and the important growth of this very active field of research in the last two decades motivate us to develop our investigation which will be based on the modern tools of variational analysis and vector optimization. Our scientific demarche refers to three classes of problems that are very important in order to emphasize new aspects in the theory of set-valued optimization and this can generate a new impetus for practical applications. Besides the intrinsic links between the problems we want to explore, an argument that unifies and increases the success chances of our study is the convergence of the objectives and methods we envisage. Another motivation for our approach is the project leader's recent book on the subject. In the last years, new aspects of the optimization problems were emphasized, which naturally required the introduction and the study of more refined variational principles and specialized regularity concepts for set-valued mappings, as different properties of subregularity, directional regularities, or fixed-set regularities. Therefore, these new aspects provided more refined tools for the study of problems with an increased degree of precision in the modeling of the real world. This is the case of vector optimization problems with variable ordering structures, a very recent area of research, with multiple applications in medical sciences, behavioral sciences and Economics. This area of research is at the core of our proposal.
2. RESEARCH TEAM
||Family and given names
||Year of birth
||Strugariu Claudiu Raducu
The main objectives of the projects are:
- (1) Variational principles for variable ordering structures and applications
- (1.1) Ekeland Variational Principle for variable ordering structures
- (1.2) Existence results in set-valued optimization with variable order
- (2) Directional metric regularity and applications to set-valued optimization
- (2.1) Coderivative conditions for directional metric regularity
- (2.2) Optimality conditions under directional metric regularity
- (3) Penalization and Aubin type properties for set-valued optimization problems
- (3.1) Vectorial penalization under vectorial Aubin conditions
- (3.2) Stability and calmness of set-valued optimization problems
4. EXPECTED RESULTS
- 1st stage of impementation (2017) - one scientific paper
- 2nd stage of impementation (2018) - two scientific papers
- 3rd stage of impementation (2019) - two scientific papers
6. INTERNATIONAL CONFERENCES
- A. Hamel, C. Zalinescu, A unified approach for EVP type results for set-valued mappings, work in progress.
- M. Durea, R. Strugariu, Optimality conditions and a barrier method in optimization with convex geometric constraint, submitted.
- International Workshop Current Trends in Applied Mathematics, Iasi, Romania, October 26-29, 2017
C. Zalinescu, On EVP type results for set-valued mappings
M. Durea, Regularity and penalization in constrained vector optimization problems
- International Conference on Applied and Pure Mathematics, Iasi, Romania, November 2-5, 2017
C. Zalinescu, Series of convex functions with applications to Statistical Mechanics
E.-A. Florea, Applications of some higher-order derivatives to generalized optimization problems
International Conference on Analysis and its Applications, Aligarh, India, November 20-22, 2017
C. Zalinescu, Convex series of convex functions with applications to
- 4th Conference on Optimization Methods and Software, Havana, Cuba, December 16-20, 2017
M. Durea, Regularity and penalization in constrained vector optimization
R. Strugariu, On some new methods to derive optimality conditions in vector optimization
8. OTHER ACTIVITIES
- C. Zalinescu: September 16 - October 6, 2017, Free University of Bozen-Bolzano, Italy, scientific collaboration with prof. dr. Andreas Hamel.
- C. Zalinescu: November 12 - 24, 2017, Aligarh, India, International Workshop on Convex Analysis and Optimization and ICAA-2017
International Conference on Analysis and its Applications.
- M. Durea: December 14-22, 2017, 4th Conference on Optimization Methods and Software, Havana, Cuba.
- R. Strugariu: December 14-22, 2017, 4th Conference on Optimization Methods and Software, Havana, Cuba.
- Regular working meetings.