Symmetric duality for minimax variational problems

Wolfe and Mond-Weir type symmetric minimax dual variational problems are formulated and usual duality theorems are established under convexity-concavity and pseudoconvexity-pseudoconcavity hypotheses respectively on the function <InlineEquation ID="Equ1"> <EquationSource Format="TEX"/> </InlineEquation> that appears in the two distinct dual pairs. Under an additional condition on the function the minimax variational problems are shown to be self duals. It is also discussed that our duality theorems can be viewed as dynamic generalization of the corresponding (static) symmetric and self duality theorems of minimax nonlinear mixed integer programming. Copyright Springer-Verlag Berlin Heidelberg 1998