Proposal's title
Research Team
Objectives
Expected results
Publications
International Conferences
Other activities
1. PROPOSAL'S TITLE
Proposal's Title: Variational Analysis over Cones and Applications to Vector Optimization
Acronym: VARACAVO
1.1 Thematic fields :
- 11 Main Sciences: Mathematics
1.2 Abstract
The research grant application we propose aims at exploring several new ideas and aspects concerning three classes of general questions in the theory of vector and set-valued optimization. The wide range of applications in various fields (including finance and machine learning) motivates our intention to generate, by the objectives and methods we envisage, a driving force for a more flexible modelling of several types of practical applications. More specifically, the main questions we propose to study are related to: variational analysis over cones, concerning the algebraic and topological properties of cones in general vector spaces; directional phenomena in Pareto efficiency, aiming a higher degree of flexibility in the possible choices of a decision maker by the use of cones of special directions; the investigation, by means of some adapted metric regularity concepts, of some numerical properties. Taking into account that the project leader is deeply involved in all the areas of research that are interconnected in the framework of this proposal (convex analysis, nonsmooth and variational analysis, set-valued optimization), and the scientific expertise of the proposed team, we believe that these objectives are achievable.
2. RESEARCH TEAM
| Nr.Crt | Family and given names | Year of birth | Scientific title | PhD |
| 1 | Zalinescu Constantin | 1952 | Professor | Yes |
| 2 | Durea Marius | 1975 | Professor | Yes |
| 3 | Strugariu Claudiu Raducu | 1978 | Professor | Yes |
| 4 | Acsinte (Florea) Elena-Andreea | 1990 | Lecturer | Yes |
| 5 | Stanciu Malina-Maria | 1997 | PhD Student | No |
| 6 | Mirciu Diana-Elena | 1999 | Master Student | No |
3. OBJECTIVES
The main objectives of the projects are:
- 1. Variational analysis over cones
- 1.1. Algebraic and topological properties of cones and variational principles
- 1.2. Cone enlargements and cone separation
- 1.3. Minimality principles in vector optimization and applications
- 2. Applications to vector optimization
- 2.1. New types of regularities for mapping and optimality conditions for Pareto efficiency
- 2.2. Stability and numerical variational analysis for Pareto efficiency
4. EXPECTED RESULTS
- 1st stage of impementation (2022) - one scientific paper
- 2nd stage of impementation (2023) - two scientific papers
- 3rd stage of impementation (2024) - two scientific papers
5. PUBLICATIONS
- M. Durea, E.-A. Florea, D. Maxim, R. Strugariu, Approximate efficiency in set-valued optimization with variable order, Journal of Nonlinear and Variational Analysis, 6 (2022), 619-640, ISI, IF - 1.683 (Q1), SRI - 0.685.
- M. Burlica, M. Durea, R. Strugariu, New concepts of directional derivatives for set-valued maps and applications to set optimization, Optimization, DOI: 10.1080/02331934.2022.2088368, ISI, IF - 1.203 (Q1), SRI - 1.124 (Q2).
- M. Durea, R. Strugariu, Directional derivatives and subdifferentials for set-valued maps applied to set optimization, Journal of Global Optimization, DOI: 10.1007/s10898-022-01222-3, ISI, IF - 0.977 (Q2), SRI - 1.211 (Q2).
- 12th International Conference on Parametric Optimization and Related Topics (paraoptXII), Augsburg, Germania, September 12-16, 2022
C. Zalinescu, On an open problem related to the parametric version of Gale's example in conic linear programming
- Regular working meetings.
- Nonlinear Analysis and Optimization Seminar.
Results 2022