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

Abstract

Based on strong efficiency instead of weak efficiency or efficiency, this paper gives the definitions and some fundamental properties of the strong supremum and infimum sets. The concepts, some properties and their relationships of s-(H,Ω) conjugate maps, s-(H,Ω)-subgradients, s- H p Γ (Ω)-regularitions of vector-valued point-to-set maps are provided, and a new duality theory in multiobjective nonlinear optimization------s-(H,Ω) Conjugate Duality Theory is established by means of the s-(H,Ω) conjugate maps. The concepts and their relationships between the strong efficient solutions of the primal and dual problems and the strong saddle-points of the s-(H,Ω)-Lagrangian map are developed. Finally, some possible further research works are given.
Key words: conjugate duality theory, multiobjective optimization, strong efficiency