ArticleOriginal scientific text
Title
Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data
Authors 1,
Affiliations
- Faculté des Sciences et Techniques, Département de Mathématiques, B.P. 618, Marrakech, Maroc
Abstract
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.
Keywords
contingent derivative, γ-paraconvex multifunction, optimality conditions, B-tangentially compact, compactly γ-paraconvex multifunction, Pareto minimal point
Bibliography
- K. Allali and T. Amahroq, On openness and regularity of γ-paraconvex multifunctions, Control Cybernet., to appear.
- 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.
- 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.
- H. W. Corley, Optimality conditions for maximizations of set valued-functions, J. Optim. Theory Appl. 58 (1988), 1-10.
- A. Jourani, Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications, Studia Math. 117 (1996), 123-136.
- D. T. Luc, Contingent derivatives of set-valued maps and applications to vector optimization, Math. Programming 50 (1991), 99-111.
- D. T. Luc and C. Malivert, Invex optimisation problems, Bull. Austral. Math. Soc. 46 (1992), 47-66.
- J. P. Penot, Differentiability of relations and differential stability of perturbed optimization problems, SIAM J. Control Optim. 22 (1984), 529-551.
- S. Rolewicz, On paraconvex multifunctions, Oper. Res. Verfahren 31 (1979), 539-546.
- S. Rolewicz, On γ-paraconvex multifunctions, Math. Japon. 24 (1979), 293-300.
- D. S. Shi, Contingent derivative of the perturbation map in multiobjective optimization, J. Optim. Theory Appl. 70 (1991), 385-396.
- A. Taa, Necessary and sufficient conditions for multiobjective optimization problems, Optimization 36 (1996), 97-104.
- T. Tanino, Sensitivity analysis in multiobjective optimization, J. Optim. Theory Appl. 56 (1988), 479-499.
Pages:
239-247
Main language of publication
English
Received
1996-06-18
Accepted
1996-08-20
Published
1997
Exact and natural sciences