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.