Optimality and duality for minmax problems involving arcwise connected and generalized arcwise connected functions

Abstract

In this paper, we establish necessary optimality conditions for a static minmax programming problem of the form:minmaxy∈Yφ(x,y) subject tog(x)≦0,in terms of the right derivatives of the functions with respect to the same arc. Various theorems giving sufficient optimality conditions are proved. A Mond-Weir type dual is proposed and duality results are established under arcwise connectedness and generalized arcwise connectedness assumptions. © 1999 Academic Press.