Titlul complet al propunerii

  Echipa de cercetare

  Obiective

  Rezultate preconizate

  Publicatii

  Conferinte Internationale

  Mobilitati

  Alte activitati

• 11 STIINTE DE BAZA: Matematica

1.2 Rezumat

Prezentul proiect de cercetare vizeaza un studiu aprofundat al problemelor de optimizare vectoriala cu multifunctii, un domeniu aflat la intersectia ariilor de cercetare ale analizei neliniare variationale si ale teoriei optimizarii. Multitudinea de aplicatii in diverse domenii (incluzand stiintele economice, inteligenta artificiala, stiintele comportamentale) precum si cresterea importanta a acestui foarte activ domeniu de cercetare in ultimele douazeci de ani ne motiveaza sa dezvoltam investigatia noastra ce va fi bazata pe uneltele moderne ale analizei variationale si optimizarii vectoriale. Demersul nostru stiintific se refera la trei clase de probleme care sunt foarte importante pentru punerea in evidenta a unor noi aspecte in teoria optimizarii cu multifunctii, acestea putand genera un nou imbold aplicatiilor practice. In afara de legaturile intrinseci dintre aceste probleme pe care dorim sa le cercetam, un alt aspect care le uneste si creste sansele de succes ale studiului nostru este convergenta obiectivelor si metodelor pe care le avem in vedere. O alta motivatie pentru abordarea noastra este recenta monografie pe subiectul prezentei propuneri a liderului de proiect. In ultimii ani noi aspecte ale problemelor de optimizare au fost evidentiate iar acestea au necesitat introducerea si studiul unor versiuni rafinate ale principiilor variationale si concepte de regularitate specializate pentru multifunctii, cum ar fi subregularitatea, regularitatea directionala sau regularitatea in raport cu o multime. Aceste noi aspecte au generat metode adaptate pentru studiul problemelor cu un grad ridicat de precizie in modelarea fenomenelor lumii reale. Acesta este si cazul problemelor de optimizare cu structuri de ordine variabila, o foarte recenta arie de cercetare cu multiple aplicatii in stiintele medicale, stiintele comportamentale si economie. Acest domeniu de cercetare este in centrul propunerii noastre.

3. OBIECTIVE

In acord cu cele precizate mai sus, obiectivele proiectului sunt:

• (1) Principii variationale pentru structuri de ordine variabile si aplicatii
  • (1.1) Principiul variational Ekeland pentru structuri de ordine variabile
  • (1.2) Rezultate de existenta in optimizarea cu multifunctii in cazul ordinii variabile
• (2) Regularitate metrica directionala si aplicatii in optimizarea cu multifunctii
  • (2.1) Conditii cu coderivate pentru regularitatea metrica directionala
  • (2.2) Conditii de optimalitate in ipoteze de regularitate metrica directionala
• (3) Penalizare si proprietati de tip Aubin in optimizarea cu multifunctii
  • (3.1) Penalizare vectoriala in ipoteze de continuitate Aubin vectoriale
  • (3.2) Stabilitate si calm pentru optimizarea cu multifunctii

• Etapa I (2017) - o lucrare stiintifica
• Etapa a II-a (2018) - doua lucrari stiintifice
• Etapa a III-a (2019) - doua lucrari stiintifice

• 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, 26-29 octombrie 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, 2-5 noiembrie 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, 20-22 noiembrie 2017
          C. Zalinescu, Convex series of convex functions with applications to statistical mechanics
  


• 4th Conference on Optimization Methods and Software, Havana, Cuba, 16-20 decembrie, 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, 18-21 iunie, 2018
          C. Zalinescu, Quadratic Minimization Problems via CDT Method
  


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


• Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germania, 28 iunie - 1 iulie, 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, Spania, 8-11 iulie, 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, Germania, 11-16 februarie, 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, Italia, 15-21 iunie, 2019
          C. Zalinescu, On unconstrained optimization problems solved using CDT and triality theory
  


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


• International Conference on Continuous Optimization, Berlin, Germania, 3-8 august, 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: 16 septembrie - 6 octombrie 2017, Free University of Bozen-Bolzano, Italia, colaborare stiintifica cu prof. dr. Andreas Hamel
  
  
• C. Zalinescu: 12 - 24 noiembrie 2017, Aligarh, India, International Workshop on Convex Analysis and Optimization si ICAA-2017 International Conference on Analysis and its Applications.
  
  
• M. Durea: 14-22 decembrie 2017, 4th Conference on Optimization Methods and Software, Havana, Cuba.
  
  
• R. Strugariu: 14-22 decembrie 2017, 4th Conference on Optimization Methods and Software, Havana, Cuba.
  
  
• C. Zalinescu: 14-25 iunie, 2018, Nonlinear Analysis and Optimization (NAOP2018), Zanjan, Iran si Workshop on Nonlinear Analysis and its Applications, Isfahan, Iran.
  
  
• C. Zalinescu: 27 iunie - 2 iulie 2018, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germania.
  
  
• M. Durea: 27 iunie - 2 iulie 2018, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germania.
  
  
• E.-A. Florea: 27 iunie - 2 iulie 2018, Colloquium & International Conference on Variational Analysis and Nonsmooth Optimization, Halle, Germania.
  
  
• M. Durea: 7-12 iulie 2018, 29th European Conference on Operational Research, Valencia, Spania.
  
  
• M. D. Pantiruc: 7-12 iulie 2018, 29th European Conference on Operational Research, Valencia, Spania.
  
  
• E.-A. Florea: 7-12 iulie 2018, 29th European Conference on Operational Research, Valencia, Spania.
  
  
• C. Zalinescu: 10 - 16 februarie, 2019, Fourth International Conference on Set Optimization and Set-Valued Variational Analysis with Applications to Economics, Finance, Statistics, Jena, Germania.
  
  
• C. Zalinescu: 13 aprilie - 7 mai, 2019, colaborare stiintifica cu Prof. Dr. Christiane Tammer, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germania.
  
  
• T. Chelmus: 18-26 mai 2019, Spring School on Variational Analysis 2019, Paseky, Republica Ceha.
  
  
• D. Plop (Maxim): 18-26 mai 2019, Spring School on Variational Analysis 2019, Paseky, Republica Ceha.
  
  
• C. Zalinescu: 15 - 22 iunie, 2019, The 3rd International Conference and Summer School Numerical Computations: Theory and Algorithms NUMTA 2019, Le Castella - Isola Capo Rizzuto Crotone, Italia.
  
  
• C. Zalinescu: 7 - 10 iulie, 2019, 6th World Congress on Global Optimization, Metz, Franta.
  
  
• M. Durea: 31 iulie - 10 august 2019, International Conference on Continuous Optimization, Berlin, Germania.
  
  
• R. Strugariu: 31 iulie - 10 august 2019, International Conference on Continuous Optimization, Berlin, Germania.
  
  
• T. Chelmus: 2-9 august 2019, International Conference on Continuous Optimization, Berlin, Germania.
  
  
• D. Plop (Maxim): 2-9 august 2019, International Conference on Continuous Optimization, Berlin, Germania.
  
  

• Intalniri periodice de lucru.


• Seminarul stiintific Analiza neliniara si optimizare.