tailieunhanh - Optimality and second order duality for a class of quasi-differentiable multiobjective optimization problem

A second order Mond-Weir type dual is presented for a non-differentiable multiobjective optimization problem with square root terms in the objective as well as in the constraints. Optimality and duality results are presented. Classes of generalized higher order η – bonvex and related functions are introduced to study the optimality and duality results. A fractional case is presented at the end. | Yugoslav Journal of Operations Research 23 (2013) Number 2, 221-235 DOI: OPTIMALITY AND SECOND ORDER DUALITY FOR A CLASS OF QUASI-DIFFERENTIABLE MULTIOBJECTIVE OPTIMIZATION PROBLEM Rishi R. SAHAY Department of Operational Research, University of Delhi-110007, India rajansahay@ Guneet BHATIA Department of Mathematics, University of Delhi-110007, India guneet172@ Received: Јаnuary 2013 / Accepted: June 2013 Abstract: A second order Mond-Weir type dual is presented for a non-differentiable multiobjective optimization problem with square root terms in the objective as well as in the constraints. Optimality and duality results are presented. Classes of generalized higher order η – bonvex and related functions are introduced to study the optimality and duality results. A fractional case is presented at the end. Keywords: Higher order η – bonvexity, Strict minimizers, Second order duality. MSC: 26A51, 90C29, 90C46. 1. INTRODUCTION The notion of second order duality was first introduced by Mangasarian [15]. The motivation behind the construction of a second order dual was the applicability in the development of algorithms for certain problems. The second order dual has computational advantage over the first order dual as it provides a tighter bound for the value of the objective function when approximations are used. One more advantage of second order duality is that, if a feasible point for the problem is provided and first order duality does not hold then, one can use a second order dual to get a lower bound for the value of primal objective function [13]. Recently, several authors [1, 2 and 14] have studied second order duality for various classes of optimization problems. . Sahay, G. Bhatia / Optimality And Second Order Duality 222 Under the assumption that means, variances and covariances of the random variables are known, Sinha [18] established a way that a stochastic linear programming problem leads to a .