Titlul complet al propunerii

  Echipa de cercetare

  Obiective

  Publicatii

• 11 STIINTE DE BAZA: Matematica

1.2 Rezumat

Proiectul este orientat pe relatiile dintre metodele si rezultatele din analiza varitionala neliniara si structura specifica a problemelor de optimizare vectoriala cu date nenetede. De fapt, tema acestui proiect face parte din domeniul mai larg al programarii neliniare cu aplicatii in economie. Aceasta tematica este importanta atat din punct de vedere teoretic, cat si practic, proiectul vizand studierea in detaliu a trei probleme, legate intre ele prin convergenta obiectivelor si a metodelor. Acestea sunt:

Stabilitate si regularitate in optimizarea vectoriala (Obiectivul 1)

Dorim sa extindem studiul asupra marginirii erorii globale pentru probleme de programare vectoriala liniara si sa investigam apoi regularitatea metrica a sistemelor variationale parametrice in cazul unei multifunctii restrictie sub forma generala, pentru a obtine noi conditii de calificare. In contrast cu cazul scalar, ne asteptam ca aceste probleme sa fie investigate prin metode si tehnici destul de diferite, deoarece avem intentia de a considera cazuri foarte generale, ce includ aplicatii multivoce atat in cazul parametric, cat si in cel neparametric.

Metode variationale in optimizarea vectoriala si aplicatii (Obiectivul 2)

In cadrul acestui obiectiv, ne propunem sa obtinem noi extensii ale Principiului Variational al lui Ekeland pentru functii si multifunctii intre spatii infinit dimensionale, precum si consecinte vizand conditii de tip Palais-Smale pentru multifunctii cu valori in spatii partial ordonate.

Analiza variationala numerica in optimizarea vectoriala (Obiectivul 3)

Avem intentia sa initiem o analiza variationala numerica a problemelor de programare vectoriala. Aceasta abordare este complet noua in optimizarea vectoriala, iar studiul nostru va urmari initial cazul scalar, dar ne asteptam sa apara numeroase probleme noi in cazul vectorial. In final, ne propunem sa obtinem o schema numerica stabila pentru anumite probleme de optimizare vectoriala cu restrictii explicite.

3. OBIECTIVE

Conform celor precizate mai sus, obiectivele proiectului sunt:

• (1) Stabilitate si regularitate in optimizarea vectoriala
  • (1a) Marginirea erorii pentru probleme de optimizare vectoriala liniara
  • (1b) Regularitate metrica si conditii de calificare
• (2) Metode variationale in optimizarea vectoriala si aplicatii
  • (2a) Extensii ale Principilui Variational Ekeland pentru multifunctii
  • (2b) Conditii de existenta si optimalitate pentru puncte de minim in optimizarea multicriteriala
• (3) Analiza variationala numerica in optimizarea vectoriala
  • (3a) Senzitivitate in probleme de optimizare vectoriala
  • (3b) Conditii de calificare stabile si conditii de optimalitate secventiala

Raport 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, Serie A, 143 (2014), 147-176 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, 159 (2013), 635-655 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, Italia, 14-22 mai, 2012
          C. Zalinescu, On separation theorems and duality results using the quasirelative interior


• International Symposium on Mathematical Programming, Berlin, Germania, 19-24 august, 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, Florenta, Italia, 26-28 iunie, 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, Roma, Italia, 1-4 iulie, 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, 7-11 Octombrie 2013
          C. Zalinescu, Relations between the convexity of a set and the differentiability of its support function
  


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


• Workshop on Optimization, Game Theory and Related Topics, Genova, Italia, 8-9 mai 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, Italia, 8-12 septembrie 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 Connference 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: mobilitate la Universite d'Avignon, Franta, in perioada 23.04.2012 - 10.04.2012; colaborare stiintifica cu Profs. D. T. Luc si M. Volle.
  
  
• R. Strugariu: participare la Spring School on Analysis 2012, Paseky, Cehia, in perioada 21.04.2012 - 29.04.2012.
  
  
• C. Zalinescu: mobilitate la Martin-Luther-Universitat Halle-Wittenberg, Halle, Germania, in perioada 2.06.2012 - 19.06.2012; colaborare stiintifica Prof. Christiane Tammer.
  
  
• M. Durea: mobilitate la Martin-Luther-Universitat Halle-Wittenberg, Halle, Germania, in perioada 19.06.2012 - 11.07.2012; colaborare stiintifica Prof. Christiane Tammer.
  
  
• Chr. Tammer (colaborator): profesor invitat la Universitatea "Al. I. Cuza", Iasi, Romania, in perioada 15.10.2012 - 24.10.2012.
  
  
• C. Zalinescu: mobilitate la Rochester Institute of Technology, Rochester, New York, USA, in perioada 9.11.2012 - 20.11.2012; colaborare stiintifica Prof. Akhtar A. Kahn.
  
  
• C. Zalinescu: mobilitate la Martin-Luther-Universitat Halle-Wittenberg, Halle, Germania, in perioada 08.04.2013 - 21.04.2013; colaborare stiintifica Prof. Christiane Tammer, pentru a finaliza o monografie scrisa in colaborare.
  
  
• C. Zalinescu: mobilitate la Rochester Institute of Technology, Rochester, New York, USA, in perioada 22.05.2013 - 2.06.2013; colaborare stiintifica Prof. Akhtar A. Kahn, pentru a finaliza o monografie scrisa in colaborare.
  
  
• C. Zalinescu: mobilitate la Martin-Luther-Universitat Halle-Wittenberg, Halle, Germania, in perioada 23.02.2014 - 9.03.2014; colaborare stiintifica Prof. Christiane Tammer.
  
  
• M. Durea: mobilitate la Universita degli Studi di Genoa, Genova, Italia, in perioada 7.05.2014 - 11.05.2014; colaborare stiintifica cu Prof. C.N. Bianchi.
  
  
• C. Zalinescu: mobilitate la Universite de Poitiers, Poitiers, Franta, in perioada 14.06.2014 - 15.07.2014; colaborare stiintifica.
  
  
• C. Zalinescu: mobilitate la Universitatea din Zurich, Zurich, Elvetia, in perioada 3.10.2014 - 7.10.2014; documentare, expunerea unor rezultate, colaborare stiintifica Prof. Diethard Klatte.
  
  
• C. Zalinescu: mobilitate la Universitatea din Viena, Viena, Austria, in perioada 7.06.2015 - 14.06.2015; documentare, expunerea unor rezultate, colaborare stiintifica Prof. Radu Ioan Bot.
  
  
• E.A. Acsinte: participare la Scuola Matematica Interuniversitaria, Perugia, Italy, in perioada 25.07.2015 - 30.08.2015.
  
  

• Sesiunea de comunicari stiintifice a Facultatii de Matematica in cadrul Zilelor Universitatii "Al. I. Cuza", octombrie 2012, Iasi.


• Seminarul de Ecuatii Diferentiale, Optimizare si Control Optimal, Facultatea de Matematica, Universitatea "Al. I. Cuza", Iasi, intalniri saptamanale.