w-(H,Ω) CONJUGATE DUALITY THEORY IN MULTIOBJECTIVE NONLINEAR OPTIMIZATION

Abstract

The duality in multiobjective optimization holds now a major position in the theory of multiobjective programming not only due to its mathematical elegance but also its economic implications. For weak efficiency instead of efficiency, this paper gives the definition and some fundamental properties of the weak supremum and infimum sets. Based on the weak supremum, the concepts, some properties and their relationships of w-(H,Ω) conjugate maps, w-(H,Ω)-subgradients, w- H p Γ (Ω)-regularitions of vector-valued point-to-set maps are provided, and a new duality theory in multiobjective nonlinear optimization------w-(H,Ω) Conjugate Duality Theory is established by means of the w-(H,Ω) conjugate maps. The concepts and their relations to the weak efficient solutions to the primal and dual problems of the w-(H,Ω)-Lagrangian map and weak saddle-point are developed. Finally, several special cases for H and Ω are discussed.
Key words: Conjugate duality theory, Multiobjective optimization, Weak efficiency