Variational principles for set-valued mappings with applications to multiobjective optimization

• Autorzy: Bao T. Q. , Mordukhovich B. S.
• Języki publikacji: EN

Abstrakty

EN

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which-being certainly of independent interest-are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang, formulated via an appropriate subdifferential notion for set-valued mappings with values in partially ordered spaces. Based on these variational principles and corresponding tools of generalized differentiation, we derive new conditions of the coercivity and Palais-Smale types ensuring the existence of optimal solutions to set-valued optimization problems with noncompact feasible sets in infinite dimensions and then obtain necessary optimality and suboptimality conditions for nonsmooth multiobjective optimization problems with general constraints, which are new in both finite-dimensional and infinite-dimensional settings.

Słowa kluczowe

EN

multiobjective optimization; variational principles; generalized differentiation; necessary optimality and suboptimality conditions

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 531--562
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Bao T. Q.

autor

Mordukhovich B. S.

• Department of Mathematics, Wayne State University, Detroit, MI 48202, USA,

Bibliografia

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