In this paper, we establish approximate Lagrangian multiplier rule, Lagrangian duality and saddle point optimality for set optimization problem where the solutions are defined using set relations introduced by Kuroiwa (Kuroiwa D., The natural criteria in set-valued optimization. Su̅rikaisekikenkyu̅sho Ko̅kyu̅roku 1031 (1998) 85–90).
Accepté le :
DOI : 10.1051/ro/2016068
Mots-clés : Set optimization, approximate solutions, Lagrangian multiplier rule, Lagrangian duality, saddle point optimality
@article{RO_2017__51_3_819_0, author = {Lalitha, C. S. and Dhingra, Mansi}, title = {Approximate {Lagrangian} duality and saddle point optimality in set optimization}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {819--831}, publisher = {EDP-Sciences}, volume = {51}, number = {3}, year = {2017}, doi = {10.1051/ro/2016068}, mrnumber = {3880527}, zbl = {1393.49013}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2016068/} }
TY - JOUR AU - Lalitha, C. S. AU - Dhingra, Mansi TI - Approximate Lagrangian duality and saddle point optimality in set optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 819 EP - 831 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2016068/ DO - 10.1051/ro/2016068 LA - en ID - RO_2017__51_3_819_0 ER -
%0 Journal Article %A Lalitha, C. S. %A Dhingra, Mansi %T Approximate Lagrangian duality and saddle point optimality in set optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 819-831 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2016068/ %R 10.1051/ro/2016068 %G en %F RO_2017__51_3_819_0
Lalitha, C. S.; Dhingra, Mansi. Approximate Lagrangian duality and saddle point optimality in set optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 819-831. doi : 10.1051/ro/2016068. http://www.numdam.org/articles/10.1051/ro/2016068/
Existence and Lagrangian duality for maximizations of set-valued functions. J. Optim. Theory Appl. 54 (1987) 489–501. | DOI | MR | Zbl
,Optimality conditions for maximizations of set-valued functions. J. Optim. Theory Appl. 58 (1988) 1–10. | DOI | MR | Zbl
,On approximate minima in vector optimization. Numer. Funct. Anal. Optim. 22 (2001) 845–859. | DOI | MR | Zbl
and ,O. Güler, Foundations of optimization. Vol. 258 of Graduate Texts in Mathematics. Springer, New York (2010). | MR | Zbl
Lagrange duality in set optimization. J. Optim. Theory Appl. 161 (2014) 368–397. | DOI | MR | Zbl
and ,Lagrangian duality in set-valued optimization. J. Optim. Theory Appl. 134 (2007) 119–134. | DOI | MR | Zbl
and ,Nonconvex scalarization in set optimization with set-valued maps. J. Math. Anal. Appl. 325 (2007) 1–18. | DOI | MR | Zbl
and ,Lagrange duality, stability and subdifferentials in vector optimization. Optimization 62 (2013) 415–428. | DOI | MR | Zbl
, , and ,Existence theorems of set optimization with set-valued maps. J. Inf. Optim. Sci. 24 (2003) 73–84. | MR | Zbl
,D. Kuroiwa, On duality of set-valued optimization, Research on nonlinear analysis and convex analysis (Japanese) (Kyoto, 1998). Srikaisekikenkysho Kkyroku 1071 (1998) 12–16. | MR | Zbl
On set-valued optimization. Nonlin. Anal. 47 (2001) 1395–1400. | DOI | MR | Zbl
,D. Kuroiwa, Some duality theorems of set-valued optimization with natural criteria, In: Proc. of the International conference on nonlinear analysis and convex analysis. World Scientific, River Edge, NJ (1999) 221–228. | MR | Zbl
D. Kuroiwa, The natural criteria in set-valued optimization. Srikaisekikenkysho Kkyroku 1031 (1998) 85–90. | MR | Zbl
Convex -programming. Sov. Math. Dokl. 20 (1979) 391–393. | Zbl
,Lagrangian multipliers, saddle points and duality in vector optimization of set-valued maps. J. Math. Anal. Appl. 215 (1997) 297–316. | DOI | MR | Zbl
and ,A. Löhne, Vector Optimization with Infimum and Supremum. Springer-Verlag, Berlin (2011). | Zbl
Lagrangian duality for vector optimization problems with set-valued mappings. Taiwanese J. Math. 17 (2013) 287–297. | MR | Zbl
and ,D.T. Luc, Theory of Vector Optimization. Vol. 319 of Lecture notes in Econom. and Math. Systems. Springer-Verlag, Berlin (1989). | MR | Zbl
-Weak minimal solutions of vector optimization problems with set-valued maps. J. Optim. Theory Appl. 106 (2000) 569–579. | DOI | MR | Zbl
and ,Duality for vector optimization of set-valued functions. J. Math. Anal. Appl. 201 (1996) 212–225. | DOI | MR | Zbl
,Lagrangian duality for minimization of nonconvex multifunctions. J. Optim. Theory Appl. 93 (1997) 167–182. | DOI | MR | Zbl
,Approximate saddle-point theorems in vector optimization. J. Optim. Theory Appl. 55 (1987) 435–448. | DOI | MR | Zbl
,Near-subconvexlikeness in vector optimization with set-valued functions. J. Optim. Theory Appl. 110 (2001) 413–427. | DOI | MR | Zbl
, and ,Cité par Sources :