On symmetric duality in mathematical programming with (b, F)-convexity

Under (b, F)–convexity, (b, F)–concavity, (b, F)–pseudoconvexity and (b, F)–pseudoconcavity, appropriate duality results for Mond–Weir type first and second order symmetric dual nonlinear programming problems are established. These duality results are then used to investigate first and second order duality for minimax versions of symmetric dual models wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, e.g., the set of integers.