Proposal's title

  Research Team

  Objectives

  Expected results

  Publications

  International Conferences

  Mobilities

  Other activities

• 11 Main Sciences: Mathematics

1.2 Abstract

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.

3. OBJECTIVES

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

• 1st stage of impementation (2017) - one scientific paper
• 2nd stage of impementation (2018) - two scientific papers
• 3rd stage of impementation (2019) - two scientific papers

• M. Durea, R. Strugariu, Optimality conditions and a barrier method in optimization with convex geometric constraint, Optimization Letters, 12 (2018), 923-931, ISI, Factor de Impact - 1.399, Scor Relativ de Influenta - 1.020.


• M. Durea, R. Strugariu, A barrier method in convex optimization with generalized inequality constraint, Optimization Letters 14 (2020), 759-769, ISI, Factor de Impact - 1.399, Scor Relativ de Influenta - 1.020.


• M. Durea, E. A. Florea, R. Strugariu, Henig proper efficiency in vector optimization with variable ordering structure, Journal of Industrial and Management Optimization, 15 (2019), 791-815, ISI, Factor de Impact - 1.025, Scor Relativ de Influenta - 0.913.


• E.-A. Florea, Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting, Journal of Optimization Theory and Applications, 178 (2018), 94-118, ISI, Factor de Impact - 1.600, Scor Relativ de Influenta - 1.447.


• T. Chelmus, M. Durea, E.-A. Florea, Directional Pareto efficiency: concepts and optimality conditions, Journal of Optimization Theory and Applications, 182 (2019), 336-365, ISI, Factor de Impact - 1.600, Scor Relativ de Influenta - 1.447.


• R. Cibulka, M. Durea, M. D. Pantiruc, R. Strugariu, On the stability of the directional regularity, Set-Valued and Variational Analysis 28 (2020), 209-237, ISI, Factor de Impact - 1.120, Scor Relativ de Influenta - 1.602.


• M. Durea, E.-A. Florea, R. Strugariu, Efficiencies and optimality conditions in vector optimization with variable ordering structure, capitol in cartea Variational Analysis and Set Optimization: Developments and Applications in Decision Making, C. Tammer, A. Khan, E. Koebis (Eds.), CRC Press (Taylor & Francis).


• C. Zalinescu, On unconstrained optimization problems solved using the canonical duality and triality theories , Optimization, ISI, Factor de Impact - 1.206, Scor Relativ de Influenta - 1.084.


• T. Chelmus, M. Durea, Exact penalization and optimality conditions for constrained directional Pareto efficiency, Pure and Applied Functional Analysis, acceptata spre publicare.


• A. Hamel, C. Zalinescu, Minimal element theorems revisited, J. Math. Anal. Appl. 486(2) (2020), ISI, Impact Factor - 1.294, Relative Influence Score - 1.104.


• C. Zalinescu, On quadratic optimization problems and canonical duality theory, Optim. Lett. ISI, Impact Factor - 1.399, Relative Influence Score - 1.020.


• E.-A. Florea, D.-E. Plop (Maxim), Directional openness for epigraphical mappings and optimality conditions for directional efficiency, Optimization. ISI, Factor de Impact - 1.206, Scor Relativ de Influenta - 1.084.


• M. Durea, R. Strugariu, On the sensitivity of Pareto efficiency in set-valued optimization problems, trimisa spre publicare.

• 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
  


• ICAA-2017 International Conference on Analysis and its Applications, Aligarh, India, November 20-22, 2017
          C. Zalinescu, Convex series of convex functions with applications to statistical mechanics
  


• 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
  


• Nonlinear Analysis and Optimization (NAOP2018), Zanjan, Iran, June 18-21, 2018
          C. Zalinescu, Quadratic Minimization Problems via CDT Method
  


• Workshop on Nonlinear Analysis and its Applications, Isfahan, Iran, June 23, 2018
          C. Zalinescu, Minimal element theorems and EVP type results for multifunctions
  


• Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germany, June 28 - July 1, 2018
          C. Zalinescu, On canonical duality theory in nonconvex optimization
          M. Durea, On directional regularity of mappings and applications to optimization
          E.-A. Florea, Vector optimization problems with generalized functional constraints in variable ordering structure setting
  


• 29th European Conference on Operational Research, Valencia, Spain, July 8-11, 2018
          M. Durea, Optimality conditions and a barrier method in convex optimization without convex representation
          M. D. Pantiruc, On the stability of the directional regularity
          E.-A. Florea, Henig efficiency in vector optimization problems with variable ordering structure
  


• Fourth International Conference on Set Optimization and Set-Valued Variational Analysis with Applications to Economics, Finance, Statistics, Jena, Germany, February 11-16, 2019
          C. Zalinescu, Minimal point theorems and variational principles in set-valued optimization
  


• The 3rd International Conference and Summer School Numerical Computations: Theory and Algorithms NUMTA 2019, Le Castella - Isola Capo Rizzuto Crotone, Italy, June 15-21, 2019
          C. Zalinescu, On unconstrained optimization problems solved using CDT and triality theory
  


• 6th World Congress on Global Optimization, Metz, France, July 8-10, 2019
          C. Zalinescu, On constrained optimization problems solved using the canonical duality theory
  


• International Conference on Continuous Optimization, Berlin, Germany, August 3-8, 2019
          M. Durea, Barrier methods for optimization problems with convex constraint
          R. Strugariu, Stability of the directional regularity
          T. Chelmus, Directional Pareto efficiency
          D.-E. Plop (Maxim), Directional minimality concepts in vector optimization
  

• 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.
  
  
• C. Zalinescu: June 14-25, 2018, Nonlinear Analysis and Optimization (NAOP2018), Zanjan, Iran, and Workshop on Nonlinear Analysis and its Applications, Isfahan, Iran.
  
  
• C. Zalinescu: June 27 -July 2, 2018, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germany.
  
  
• M. Durea: June 27 -July 2, 2018, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germany.
  
  
• E.-A. Florea: June 27 -July 2, 2018 Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germany.
  
  
• M. Durea: July 7-12, 2018, 29th European Conference on Operational Research, Valencia, Spain.
  
  
• M. D. Pantiruc: July 7-12, 2018, 29th European Conference on Operational Research, Valencia, Spain.
  
  
• E.-A. Florea: July 7-12, 2018, 29th European Conference on Operational Research, Valencia, Spain.
  
  
• C. Zalinescu: February 10 - 16, 2019, Fourth International Conference on Set Optimization and Set-Valued Variational Analysis with Applications to Economics, Finance, Statistics, Jena, Germany.
  
  
• C. Zalinescu: April 13 - May 7, 2019, scientific collaboration with Prof. Dr. Christiane Tammer, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany.
  
  
• T. Chelmus: May 18-26, 2019, Spring School on Variational Analysis 2019, Paseky, Czech Republic.
  
  
• D. Plop (Maxim): May 18-26, 2019, Spring School on Variational Analysis 2019, Paseky, Czech Republic.
  
  
• C. Zalinescu: June 15 - 22, 2019, The 3rd International Conference and Summer School Numerical Computations: Theory and Algorithms NUMTA 2019, Le Castella - Isola Capo Rizzuto Crotone, Italy.
  
  
• C. Zalinescu: July 7 - 10, 2019, 6th World Congress on Global Optimization, Metz, France.
  
  
• M. Durea: July 31-August 10, 2019, International Conference on Continuous Optimization, Berlin, Germany.
  
  
• R. Strugariu: July 31-August 10, 2019, International Conference on Continuous Optimization, Berlin, Germany.
  
  
• T. Chelmus: August 2-9, 2019, International Conference on Continuous Optimization, Berlin, Germany.
  
  
• D. Plop (Maxim): August 2-9, 2019, International Conference on Continuous Optimization, Berlin, Germany.
  
  

• Regular working meetings.


• Nonlinear Analysis and Optimization Seminar.