EXPLORATORY RESEARCH PROJECT PNIIIDPCE201130084, nr. 239/05.10.2011
Director: Prof. dr. Constantin ZALINESCU
Proposal's title
Research Team
Objectives
Publications
International Conferences
Mobilities
Other activities
1. PROPOSAL'S TITLE
Proposal's Title: Regularity and sensitivity in multicriteria optimization
Acronym: PNIIIDPCE201130084
1.1 Thematic fields :
 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 vectorlinear 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 setvalued 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 setvalued and singlevalued mappings in infinitedimensional spaces are envisaged together with their consequences concerning PalaisSmale type conditions for setvalued 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.
2. RESEARCH TEAM
Crt Nr. 
Family and given names 
Year of birth 
Scientific title 
PhD 
1 
Durea Marius 
1975 
Associate Professor 
Yes 
2 
Strugariu Claudiu Raducu 
1978 
Associate Professor 
Yes 
4 
Acsinte ElenaAndreea 
1990 
Researcher 
No 
3. OBJECTIVES
As mentioned before, the main objectives of the projects are:
 (1) Stability and regularity in vector optimization
 (1a) Error bounds for vectorlinear programming
 (1b) Metric regularity and constraint qualification conditions
 (2) Variational methods in vector optimization and applications
 (2a) Extensions of Ekeland Variational Principle for setvalued 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
Report 2012
 M. Durea, R. Strugariu, Chain rules for linear openness in general Banach spaces, SIAM Journal on Optimization, 22 (2012), 899913 ISI, Impact Factor 2012  2,076, Relative Influence Score  3,456.
 M. Durea, R. Strugariu, Calculus of tangent sets and derivatives of setvalued maps under metric subregularity conditions, Journal of Global Optimization, 56 (2013), 587603 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/s1010701205988 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, SetValued Var. Anal., 21 (2013), 405430 ISI, Impact Factor 2012  1,036, Relative Influence Score  1,225.

M. Volle, J.B. HiriartUrruty, C. Zalinescu , When some variational properties force convexity, ESAIM Control Optim. Calc. Var., 19 (2013), 701709 ISI, Impact Factor 2012  1,282, Relative Influence Score  1,899.
Report 2013

M. Durea, H. T. Nguyen, R. Strugariu, Metric regularity of epigraphical multivalued mappings and applications to vector optimization, Mathematical Programming Serie B, 139 (2013), 139159 ISI, Impact Factor 2012  2,090, Relative Influence Score  3,782.

M. Apetrii, M. Durea, R. Strugariu, On subregularity properties of setvalued mappings, SetValued and Variational Analysis, 21 (2013), 93126 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/s1095701303602 ISI, Impact Factor 2012  1,423, Relative Influence Score  1,222.

C. Zalinescu, On some extension theorems for setvalued mappings, Nonlinear Analysis, 88 (2013) 2426 ISI, Impact Factor 2012  1,64, Relative Influence Score  1,086.
Report 2014

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, Setvalued Optimization  An Introduction with Applications, Springer, Berlin, 2015 .

C. Zalinescu, On the use of the quasirelative interior in optimization, Optimization, 64 (2015), 17951823.ISI, Impact Factor 2013  0,936, Relative Influence Score  0,867.
Report 2015
 Vu Anh Tuan, Chr. Tammer, C. Zalinescu, The Lipschitzianity of convex vector and setvalued functions, TOP, 24 (2016), 273299, ISI, Impact Factor 2014  0,831, Relative Influence Score  0,836.
 M. Durea, R. Strugariu, Metric Subregularity of Composition SetValued Mappings with Applications to Fixed Point Theory, SetValued and Variational Analysis, 24 (2016), 231251, 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), 535561, ISI, Impact Factor 2014  1.624, Relative Influence Score  1.978.
 C. Zalinescu, On the use of semiclosed sets and functions in convex analysis, Open Math. 2015; 13: 15, DOI 10.1515/math20150001, ISI, Impact Factor 2014  0.578.
 C. Zalinescu, On three open problems related to quasi relative interior, Journal of Convex Analysis, 22 (2015), 641645, ISI, Impact Factor 2014  0.552, Relative Influence Score  0.84.
Report 2016
 C. Zalinescu, On second order generalized convexity, Journal of Optimization Theory and Applications, 168 (2016), 802829, 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), Studniarskitype derivative calculus and optimality conditions in vector optimization, submitted.
5. INTERNATIONAL CONFERENCES
 58th Workshop "Variational Analysis and Applications", Erice, Italy, May 1422, 2012
C. Zalinescu, On separation theorems and duality results using the quasirelative interior
 International Symposium on Mathematical Programming, Berlin, Germany, August 1924, 2012
M. Durea, Metric regularity and Fermat rules in setvalued optimization
R. Strugariu, Metric regularity and subregularity of setvalued 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 2628, 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, 14 July, 2013
M. Durea, Calculus of tangent sets and derivatives of setvalued maps under metric subregularity conditions
R. Strugariu, Metric regularity of composition setvalued mappings. Applications to vector optimization
C. Zalinescu, FenchelRockafellar type formulas for the approximate weak subdifferential of setvalued mappings
 XI Seminario Internacional de Optimization y Areas Affines, Lima, Peru, October 711, 2013
C. Zalinescu, Relations between the convexity of a set and the
differentiability of its support function
 6th GermanPolish 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 89, 2014
M. Durea, Metric regularity and penalization in vector optimization
 International Conference on SetValued Variational Analysis and Optimization with Applications in Finance, BruneckBrunico, Italy, September 812, 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 2527, 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 1215, 2015
R. Strugariu, Metric (sub)regularity of composition setvalued mappings with applications to optimization problems with variable ordering structure
 Mathematical Optimisation Down Under (MODU2016), Melbourne, Australia, July 1822, 2016
C. Zalinescu, Convex series of convex functions with applications to Statistical Mechanics
 International Conference on Continuous Optimization (ICCOPT2016), Tokyo, Japan, August 611, 2016
M. Durea, Minimal Time Function with Respect to a Set of Directions and Applications
6. MOBILITIES
 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 MartinLutherUniversitat HalleWittenberg, Halle, Germany, in the period 2.06.2012  19.06.2012; scientific collaboration with Prof. Christiane Tammer.
 M. Durea: mobility at MartinLutherUniversitat HalleWittenberg, 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 MartinLutherUniversitat HalleWittenberg, 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 MartinLutherUniversitat HalleWittenberg, 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.
7. OTHER ACTIVITIES
 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.
Results 2011
Results 2012
Results 2013
Results 2014
Results 2015
Results 2016
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