Higher-order Symmetric Multiobjective Duality Involving Generalized (original) (raw)

Beside the well known Wolfe dual [10], Mond and Weir [14] proposed a number of different duals for nonlinear programming problems with nonnegative variables and proved various duality theorems under appropriate pseudoconvexity / quasi-convexity assumptions. The study of second order duality is significant due to the computational advantage over first order duality as it provides tighter bounds for the value of the objective function when approximations are used [7, 9, 12, 19]. Mangasarian [9] considered a nonlinear programming and discussed second order duality under inclusion condition. Mond [12] was the first who present second order convexity. He also gave in [12] simpler conditions than these of Mangasarian using a generalized form of convexity which was later called second order convexity by Mahajan [8] and bonvexity by Bector and Chandra [3]. Zhang and Mond [20] established some duality theorems for second-order duality in nonlinear programming under second order B-invexity or...