We study multiobjective optimization problems with γ-paraconvex multifunction data. Sufficient optimality conditions for unconstrained and constrained problems are given in terms of contingent derivatives.
@article{bwmeta1.element.bwnjournal-article-smv124i3p239bwm,
author = {T. Amahroq and A. Taa},
title = {Sufficient conditions of optimality for multiobjective optimization problems with $\gamma$-paraconvex data},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {239-247},
zbl = {0882.90115},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv124i3p239bwm}
}
Amahroq, T.; Taa, A. Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data. Studia Mathematica, Tome 122 (1997) pp. 239-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i3p239bwm/
[00000] [1] K. Allali and T. Amahroq, On openness and regularity of γ-paraconvex multifunctions, Control Cybernet., to appear. | Zbl 0891.49008
[00001] [2] T. Amahroq and L. Thibault, On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems, Numer. Funct. Anal. Optim. 16 (1995), 1293-1307. | Zbl 0857.49011
[00002] [3] J. P. Aubin, Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions, Adv. in Math. Suppl. Stud. 7a, L. Nachbin (ed.), Academic Press, New York, 1981, 159-229.
[00003] [4] H. W. Corley, Optimality conditions for maximizations of set valued-functions, J. Optim. Theory Appl. 58 (1988), 1-10. | Zbl 0956.90509
[00004] [5] A. Jourani, Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications, Studia Math. 117 (1996), 123-136. | Zbl 0841.46002
[00005] [6] D. T. Luc, Contingent derivatives of set-valued maps and applications to vector optimization, Math. Programming 50 (1991), 99-111. | Zbl 0718.90080
[00006] [7] D. T. Luc and C. Malivert, Invex optimisation problems, Bull. Austral. Math. Soc. 46 (1992), 47-66. | Zbl 0755.90072
[00007] [8] J. P. Penot, Differentiability of relations and differential stability of perturbed optimization problems, SIAM J. Control Optim. 22 (1984), 529-551. | Zbl 0552.58006
[00008] [9] S. Rolewicz, On paraconvex multifunctions, Oper. Res. Verfahren 31 (1979), 539-546. | Zbl 0403.49021
[00009] [10] S. Rolewicz, On γ-paraconvex multifunctions, Math. Japon. 24 (1979), 293-300. | Zbl 0434.54009
[00010] [11] D. S. Shi, Contingent derivative of the perturbation map in multiobjective optimization, J. Optim. Theory Appl. 70 (1991), 385-396. | Zbl 0743.90092
[00011] [12] A. Taa, Necessary and sufficient conditions for multiobjective optimization problems, Optimization 36 (1996), 97-104. | Zbl 0858.90112
[00012] [13] T. Tanino, Sensitivity analysis in multiobjective optimization, J. Optim. Theory Appl. 56 (1988), 479-499. | Zbl 0619.90073