Approximate Optimality Conditions in Fractional Semi-Infinite Multiobjective Optimization (Study on Nonlinear Analysis and Convex Analysis)

This paper is based on the manuscript "Approximate necessary optimality in fractional semi-infinite multiobjective optimization" written by T. Shitkovskaya, Z. Hong, D.S. Kim and G.R. Piao, which was accepted to J. Nonlinear Convex Anal.This paper provides some new results on weak approximate solutions in fractional multiobjective optimization problems. Specifically, we establish necessary optimality conditions of Fritz-John type for a local weakly E-efficient solution in fuzzy form and, by using limiting constraint qualification, we provide necessary optimality conditions of Karush-Kuhn-Tucker type for a weakly E-quasi-efficient solution. To this purpose advanced tools of variational analysis and generalized differentiation are used

On optimality conditions in nonsmooth semi-infinite vector optimization problems (Study on Nonlinear Analysis and Convex Analysis)

In this paper, we establish optimality conditions (both necessary and sufficient) for a nonsmooth semi-infinite vector optimization problem by using the scalarization method

On optimality conditions in robust optimization problems with locally Lipschitz constraints (Study on Nonlinear Analysis and Convex Analysis)

This paper is based on the published one "Approximate optimality conditions for robust convex optimization without convexity of constraints. Linear and Nonlinear Analysis 5 (2019), no.1, 173-182" written by Z. Hong, L.G. Jiao and D.S. Kim.In this paper, we study a convex optimization problem which minimizes a convex function over a convex feasible set defined by finitely many locally Lipschitz constraints (not necessarily convex or differentiable) in the face of data uncertainty. Under a non-degeneracy condition and the Slater constraint qualification, we present Karush-Kuhn-Tucker optimality conditions for the robust convex optimization problem. Moreover, we apply the obtained results to study the KKT optimality conditions for a quasi E-solution to the robust convex optimization problem

Optimality and duality for a class of nonsmooth fractional multiobjective optimization problems (Nonlinear Analysis and Convex Analysis)

In this paper, we establish necessary optimality conditions for (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with inequality and equality constraints by employing some advanced tools of variational analysis and generalized differentiation. Sufficient optimality conditions for such solutions to the considered problem are also provided by means of introducing (strictly) convex-affine functions. Along with optimality conditions, we formulate a dual problem to the primal one and explore weak, strong and converse duality relations between them under assumptions of (strictly) convex-affine functions