Duality for nonsmooth mathematical programming problems with equilibrium constraints

Abstract

Abstract In this paper, we consider the mathematical programs with equilibrium constraints (MPECs) in Banach space. The objective function and functions in the constraint part are assumed to be lower semicontinuous. We study the Wolfe-type dual problem for the MPEC under the convexity assumption. A Mond-Weir-type dual problem is also formulated and studied for the MPEC under convexity and generalized convexity assumptions. Conditions for weak duality theorems are given to relate the MPEC and two dual programs in Banach space, respectively. Also conditions for strong duality theorems are established in an Asplund space.

Keywords

• mathematical programming problems with equilibrium constraints
• Wolfe-type dual
• Mond-Weir dual
• convexity
• nonsmooth analysis