Second order symmetric duality in mathematical programming with F-convexity

Abstract

Under second order F-convexity F-concavity and second order F-pseudoconvexity F-pseudoconcavity, appropriate second order duality results for pair of Wolfe and Mond–Weir type second order symmetric dual nonlinear programming problems are established. These second order duality results are then used to formulate Wolfe type and Mond–Weir type second order minimax mixed integer dual programs and symmetric duality theorem is established under separability and second order F-convexity F-concavity of the kernel function f( x, y). Second order symmetric dual fractional mixed integer programs are studied using the above programs. Moreover, second order self-duality theorems for the above pairs are obtained assuming f( x, y) to be skew symmetric.