Proposal's title

  Research Team

  Objectives

  Publications

• 11 Main Sciences: Mathematics

1.2 Abstract

The present proposal is focused on the relationships between the methods and results of nonlinear and variational analysis and the specific structure of vector optimization problems governed by nonsmooth data. In fact, the topic of this project is a part of the general domain of nonlinear programming with applications in Economics. This field is very important from theoretical as well as from practical point of view and our project refers to three detailed research problems within this area which are unified by convergence of objectives and methods. The main objectives are:

Stability and regularity in vector optimization (Task 1)

We aim to extend the study of the global error bounds for vector-linear programming and further investigate the metric regularity of parametric variational systems in the case of a general field map in order to get new constraint qualification conditions. In contrast to the scalar case, these questions will be investigated under fairly different methods and tools because our intention is to tackle far more general cases including the set-valued data both for parametric and non parametric settings.

Variational methods in vector optimization and applications (Task 2)

Within this objective, new extensions of the Ekeland Variational Principle for set-valued and single-valued mappings in infinite-dimensional spaces are envisaged together with their consequences concerning Palais-Smale type conditions for set-valued mappings with values in partially ordered spaces. This research will rely on the project leader former works in this direction and a deep and comprehensive analysis of Vector Variational Principles, would become the basis for new existence conditions for minima of general vector optimization problems.

Numerical variational analysis in vector optimization (Task 3)

Within this objective we shall perform a numerical variational analysis of generalized vectorial programs. This is an entire new approach in vector optimization, and our study will initially follow the scalar case, but we expect to face many problems specific to the vector case. Finally, we expect to get thus a stable numerical scheme for some general vector optimization problems under explicit constraints.

• (1) Stability and regularity in vector optimization
  • (1a) Error bounds for vector-linear programming
  • (1b) Metric regularity and constraint qualification conditions
• (2) Variational methods in vector optimization and applications
  • (2a) Extensions of Ekeland Variational Principle for set-valued mappings
  • (2b) Conditions of existence and optimality for minima in vector optimization
• (3) Numerical variational analysis in vector optimization
  • (3a) Sensitivity in vector optimization problems
  • (3b) Stable constraint qualifications and sequential optimality conditions

4. PUBLICATIONS

Report 2011

• M. Durea, R. Strugariu, On parametric vector optimization via metric regularity of constraint systems, Mathematical Methods of Operations Research, 74 (2011), 409-425 ISI, Impact Factor 2012 - 0,314, Relative Influence Score - 0,963.

• M. Durea, R. Strugariu, Chain rules for linear openness in general Banach spaces, SIAM Journal on Optimization, 22 (2012), 899-913 ISI, Impact Factor 2012 - 2,076, Relative Influence Score - 3,456.


• M. Durea, R. Strugariu, Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions, Journal of Global Optimization, 56 (2013), 587-603 ISI, Impact Factor 2012 - 1,307, Relative Influence Score - 1,273.


• M. Durea, R. Strugariu, Chain rules for linear openness in metric spaces and applications, Mathematical Programming Serie A, DOI: 10.1007/s10107-012-0598-8 ISI, Impact Factor 2012 - 2,090, Relative Influence Score - 3,782.


• N. M. Nam, C. Zalinescu , Variational analysis of directional minimal time functions and applications to location problems, Set-Valued Var. Anal., 21 (2013), 405-430 ISI, Impact Factor 2012 - 1,036, Relative Influence Score - 1,225.


• M. Volle, J.-B. Hiriart-Urruty, C. Zalinescu , When some variational properties force convexity, ESAIM Control Optim. Calc. Var., 19 (2013), 701-709 ISI, Impact Factor 2012 - 1,282, Relative Influence Score - 1,899.

• M. Durea, H. T. Nguyen, R. Strugariu, Metric regularity of epigraphical multivalued mappings and applications to vector optimization, Mathematical Programming Serie B, 139 (2013), 139-159 ISI, Impact Factor 2012 - 2,090, Relative Influence Score - 3,782.


• M. Apetrii, M. Durea, R. Strugariu, On subregularity properties of set-valued mappings, Set-Valued and Variational Analysis, 21 (2013), 93-126 ISI, Impact Factor 2012 - 1,036, Relative Influence Score - 1,225.


• M. Durea, R. Strugariu, Chr. Tammer, Scalarization in geometric and functional vector optimization revisited, Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-013-0360-2 ISI, Impact Factor 2012 - 1,423, Relative Influence Score - 1,222.


• C. Zalinescu, On some extension theorems for set-valued mappings, Nonlinear Analysis, 88 (2013) 24-26 ISI, Impact Factor 2012 - 1,64, Relative Influence Score - 1,086.

• M. Apetrii, M. Durea, R. Strugariu, A new penalization tool in scalar and vector optimizations, Nonlinear Analysis, 107 (2014), 22 - 33 ISI, Impact Factor 2013 - 1,622, Relative Influence Score - 1,225.


• A. A. Khan, Chr. Tammer, C. Zalinescu, Set-valued Optimization - An Introduction with Applications, Springer, Berlin, 2015 .


• C. Zalinescu, On the use of the quasi-relative interior in optimization, Optimization, 64 (2015), 1795-1823.ISI, Impact Factor 2013 - 0,936, Relative Influence Score - 0,867.

• Vu Anh Tuan, Chr. Tammer, C. Zalinescu, The Lipschitzianity of convex vector and set-valued functions, TOP, 24 (2016), 273-299, ISI, Impact Factor 2014 - 0,831, Relative Influence Score - 0,836.


• M. Durea, R. Strugariu, Metric Subregularity of Composition Set-Valued Mappings with Applications to Fixed Point Theory, Set-Valued and Variational Analysis, 24 (2016), 231-251, ISI, Impact Factor 2014 - 1,379, Relative Influence Score - 1,652.


• 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 - 1.978.


• C. Zalinescu, On the use of semi-closed sets and functions in convex analysis, Open Math. 2015; 13: 1-5, DOI 10.1515/math-2015-0001, ISI, Impact Factor 2014 - 0.578.


• C. Zalinescu, On three open problems related to quasi relative interior, Journal of Convex Analysis, 22 (2015), 641-645, ISI, Impact Factor 2014 - 0.552, Relative Influence Score - 0.84.

• C. Zalinescu, On second order generalized convexity, Journal of Optimization Theory and Applications, 168 (2016), 802-829, ISI, Impact Factor 2015 - 1.16, Relative Influence Score - 1.164.


• C. Zalinescu, On the entropy minimization problem in Statistical Mechanics, submitted.


• E.A. Axinte (Florea), Studniarski-type derivative calculus and optimality conditions in vector optimization, submitted.

• 58th Workshop "Variational Analysis and Applications", Erice, Italy, May 14-22, 2012
          C. Zalinescu, On separation theorems and duality results using the quasirelative interior


• International Symposium on Mathematical Programming, Berlin, Germany, August 19-24, 2012
          M. Durea, Metric regularity and Fermat rules in set-valued optimization
          R. Strugariu, Metric regularity and subregularity of set-valued mappings with applications to vector optimization
          C. Zalinescu, Variational principles for multifunctions and applications
  


• 11th Europt Workshop on Advances in Continuous Optimization, Florence, Italy, June 26-28, 2013
          M. Durea, Chain rules for linear openness and applications to metric regularity of solution mapping for some mathematical programs
  


• 26th European Conference on Operations Research, Rome, Italy, 1-4 July, 2013
          M. Durea, Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions
          R. Strugariu, Metric regularity of composition set-valued mappings. Applications to vector optimization
          C. Zalinescu, Fenchel-Rockafellar type formulas for the approximate weak subdifferential of set-valued mappings
  
• XI Seminario Internacional de Optimization y Areas Affines, Lima, Peru, October 7-11, 2013
          C. Zalinescu, Relations between the convexity of a set and the differentiability of its support function
  


• 6th German-Polish Conference on Optimization, Wittenberg, Germany, February 28 - March 4, 2014
          C. Zalinescu, Convexity of a set versus differentiability of its support function
  


• Workshop on Optimization, Game Theory and Related Topics, Genova, Italy, May 8-9, 2014
          M. Durea, Metric regularity and penalization in vector optimization
  


• International Conference on Set-Valued Variational Analysis and Optimization with Applications in Finance, Bruneck-Brunico, Italy, September 8-12, 2014
          C. Zalinescu, Series of convex functions in locally convex spaces: subdiferential, conjugate and applications
  


• 3rd International Conference on Nonlinear Analysis and Optimization, Isfahan, Iran, May 25-27, 2015
          C. Zalinescu, Series of convex functions: subdifferential, conjugate and applications to entropy minimization in Statistical Physics
  


• 27th European Conference on Operational Research, University of Strathclyde, Glasgow, July 12-15, 2015
          R. Strugariu, Metric (sub)regularity of composition set-valued mappings with applications to optimization problems with variable ordering structure
  


• Mathematical Optimisation Down Under (MODU2016), Melbourne, Australia, July 18-22, 2016
          C. Zalinescu, Convex series of convex functions with applications to Statistical Mechanics
  


• International Conference on Continuous Optimization (ICCOPT2016), Tokyo, Japan, August 6-11, 2016
          M. Durea, Minimal Time Function with Respect to a Set of Directions and Applications
  

• C. Zalinescu: mobility at Universite d'Avignon, France, in the period 23.04.2012 - 10.04.2012; scientific collaboration with Profs. D. T. Luc and M. Volle.
  
  
• R. Strugariu: participation at Spring School on Analysis 2012, Paseky, Chech Republic, in the period 21.04.2012 - 29.04.2012.
  
  
• C. Zalinescu: mobility at Martin-Luther-Universitat Halle-Wittenberg, Halle, Germany, in the period 2.06.2012 - 19.06.2012; scientific collaboration with Prof. Christiane Tammer.
  
  
• M. Durea: mobility at Martin-Luther-Universitat Halle-Wittenberg, Halle, Germany, in the period 19.06.2012 - 11.07.2012; scientific collaboration with Prof. Christiane Tammer.
  
  
• Chr. Tammer (collaborator): invited professor at "Al. I. Cuza" University of Iasi, Romania, in the period 15.10.2012 - 24.10.2012.
  
  
• C. Zalinescu: mobility at Rochester Institute of Technology, Rochester, New York, USA, in the period 9.11.2012 - 20.11.2012; scientific collaboration with Prof. Akhtar A. Kahn.
  
  
• C. Zalinescu: mobility at Martin-Luther-Universitat Halle-Wittenberg, Halle, Germany, in the period 08.04.2013 - 21.04.2013; scientific collaboration with Prof. Christiane Tammer, in order to finalize a jointly written monograph.
  
  
• C. Zalinescu: mobility at Rochester Institute of Technology, Rochester, New York, USA, in the period 22.05.2013 - 2.06.2013; scientific collaboration with Prof. Akhtar A. Kahn, in order to finalize a jointly written monograph.
  
  
• C. Zalinescu: mobility at Martin-Luther-Universitat Halle-Wittenberg, Halle, Germany, in the period 23.02.2014 - 9.03.2014; scientific collaboration with Prof. Christiane Tammer.
  
  
• M. Durea: mobility at Universita degli Studi di Genoa, Genova, Italia, in the period 7.05.2014 - 11.05.2014; scientific collaboration with Prof. C.N. Bianchi.
  
  
• C. Zalinescu: mobility at Universite de Poitiers, Poitiers, Franta, in the period 14.06.2014 - 15.07.2014; scientific collaboration.
  
  
• C. Zalinescu: mobility at University of Zurich, Zurich, Switzerland, in the period 3.10.2014 - 7.10.2014; documentation, exposition of results, scientific collaboration with Prof. Diethard Klatte.
  
  
• C. Zalinescu: mobility at University of Zurich, Zurich, Switzerland, in the period 3.10.2014 - 7.10.2014; documentation, exposition of results, scientific collaboration with Prof. Diethard Klatte.
  
  
• C. Zalinescu: mobility at University of Viena, Viena, Austria, in the period 7.06.2015 - 14.06.2015; documentation, exposition of results, scientific collaboration with Prof. Radu Ioan Bot.
  
  
• E.A. Acsinte: participation at Scuola Matematica Interuniversitaria, Perugia, Italy, in the period 25.07.2015 - 30.08.2015.
  
  

• Sessions of Scientific Communications of Faculty of Mathematics Zilele Universitatii "Al. I. Cuza", October 2012, Iasi.


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