Duality in Nondifferentiable Multiobjective Fractional Programs Involving Cones

Abstract

In this paper, we introduce nondifferentiable multiobjective fractional programming problems with cone constraints over arbitrary closed convex cones, where every component of the objective function contains a term involving the support function of a compact convex set. For this problem, Wolfe and Mond-Weir type duals are proposed. We establish weak and strong duality theorems for a weakly efficient solution under suitable (V, ρ)-invexity assumptions. As special cases of our duality relations, we give some known duality results.

OPTIMALITY AND DUALITY IN NONDIFFERENTIABLE MULTIOBJECTIVE FRACTIONAL PROGRAMMING USING Α-Univexity

“…The following lemma giving necessary optimality conditions will be used in the sequel. The lemma is cited in [10] and can be obtained from [2] and [9]. Lemma 3.1.…”

“…are (multiobjective) fractional programming problems. Extensive researches have been reported in the literature for the multiobjective nonlinear (nondifferentiable) fractional programming problems involving generalized convex functions by various authors, for details see ( [1,4,[6][7][8][9][10][11][12][13]15,[18][19][20][21]) and references therein. The areas which have been explored are mainly to weaken the convexity and to relax the differentiability assumption of the functions used in developing optimality and duality of the above programming problems.…”

“…Kim et al [9] established necessary and sufficient optimality conditions and proved duality results for weakly efficient solutions of multiobjective fractional programming problem containing support functions under the assumption of (V, ρ) invex functions. Later in [10], Kim et al established duality results using (V, ρ) invexity for the same problem with cone constraints.…”

Second Order Duality in Multiobjective Fractional Programming with Square Root Term under Generalized Univex Function

“…Mond [ 25 ] considered a nonlinear fractional programming problem involving square roots of positive semidefinite quadratic form in the numerator and denominator and proved the necessary and sufficient condition for optimality. Kim et al [ 26 , 27 ] formulated a nondifferentiable multiobjective fractional problem in which numerators contain support function. One of the most known approaches used for solving nonlinear fractional programming problem is called parametric approach.…”