Proposal's title

  Research Team

  Objectives

  Expected results

  Publications

• 11 Main Sciences: Mathematics

1.2 Abstract

The present proposal is focused on the study of set-valued vector optimization problems, which belongs to the wider topic of nonlinear variational analysis, with many applications from theoretical, as well as from practical point of view. We propose ourselves to study generalized regularity properties and optimality for set-valued maps with applications to the investigation of equilibrium problems and Pareto efficiency with variable ordering structure. To this aim, we envisage the study of several variational methods in vector optimization which, on one hand, will lead to extensions of several very important results (such as Ekeland Variational Principle) for set-valued maps and variable ordering structures and, on the other hand, will offer new tools for investigation of generalized vector problems. Therefore, these results will be applied to the study of optimization problems with constraints given by partial differential equations, which model many practical situations issued from engineering, medicine, economics and behavioural sciences.

• (1) Generalized regularity and optimality for set-valued functions
  • (1.1) The study of generalized regularity properties for set-valued functions
  • (1.2) Optimality conditions in equilibrium and Pareto optimization problems with variable ordering structure
• (2) Variational methods in vector optimization and applications
  • (2.1) Extensions of Ekeland's Variational Principle for set-valued functions and variable ordering structures
  • (2.2) Applications to the study of vector optimization problems with restrictions given by partial differential equations.

4. EXPECTED RESULTS

• 1st stage of impementation (2015) - one scientific paper
• 2nd stage of impementation (2016) - two scientific papers
• 3rd stage of impementation (2017) - two scientific papers

• M. Durea, M. Pantiruc, R. Strugariu, Minimal time function with respect to a set of directions. Basic properties and applications, Optimization Methods and Software, 31 (2016), 535-561, ISI, Impact Factor 2014 - 1.624, Relative Influence Score 2015 - 1.978.


• E.-A. Florea, Coderivative necessary optimality conditions for sharp and robust efficiencies in vector optimization with variable ordering structure, Optimization, 65 (2016), 1417-1435, ISI, Impact Factor 2015 - 0.822, Relative Influence Score 2016 - 0.787.


• M. Durea, R. Strugariu, Generalized penalization and maximization of vectorial nonsmooth functions, Optimization, 66 (2017), 903-915, ISI, Impact Factor 2016 - 0.943, Relative Influence Score 2017 - 0.971.


• M. Durea, M. Pantiruc, R. Strugariu,A new type of directional regularity for mappings and applications to optimization, SIAM Journal on Optimization, 27 (2017), 1204-1229, ISI, Impact Factor 2016 - 2.765, Relative Influence Score 2017 - 4.284.


• M. Durea, R. Strugariu, Vectorial penalization for generalized functional constrained problems, Journal of Global Optimization, 68 (2017), 899-923, ISI, Impact Factor 2016 - 1.733, Relative Influence Score 2017- 1.372.


• M. Durea, R. Strugariu, C. Tammer, On some methods to derive necessary and sufficient optimality conditions in vector optimization, Journal of Optimization Theory and Applications, online first, DOI: 10.1007/s10957-016-1059-y, ISI, Impact Factor 2016 - 1.289, Relative Influence Score 2017 - 1.423.


• M.-D. Burlica, A. Paicu, D. Rosu, Compact + Lipschitz perturbations of generators of weakly equicontinuous semigroups subjected to nonlocal initial conditions, ready for submission.

• "International Conference on Pure and Applied Mathematics", Iasi, Romania, November 6-8, 2015
          M. Durea, Penalization and Metric Regularity in Vector Optimization
          M. Pantiruc, Minimal time function with respect to a set of directions
  


• "28th European Conference on Operational Research", Poznan, Poland, July 3-6, 2016
          M. Durea, Penalization Techniques and Optimality Conditions in Vector Optimization
          M. Pantiruc, Minimal Time Function with Respect to a Set of Directions
          E.-A. Florea, Optimality Conditions for Sharp and Robust Efficiencies in Vector Optimization with Variable Ordering Structure
  


• "The fifth International Conference on Continuous Optimization", Tokyo, Japon, August 6-11, 2016
          M. Durea, Minimal Time Function with Respect to a Set of Directions and Applications
  


• "XIII-eme Colloque Franco-Roumain de Mathématiques Appliquées", Iasi, Romania, August 25-29, 2016
          M. Durea, Regularities and subregularities with respect to fixed sets and applications
  


• "Workshop on Variational Analysis, Equilibria and Optimization", Pisa, Italy, May 29-30, 2017
          M. Durea, Directional approach to regularity of mappings and applications to optimization
  


• "Workshop on Variational Analysis, Equilibria and Optimization", Pisa, Italy, May 29-30, 2017
          R. Strugariu, Composition set-valued mappings: metric (sub)regularity and fixed points
  

• E.-A. Florea: participation at "International Summer School on Set Optimization for Applications ", Bozen, Italy, June 21 - July 01, 2017


• Optimization and Optimal Control Seminar, Faculty of Mathematics, "Al. I. Cuza" University of Iasi, periodical meetings.