On the Mangasarian–Fromovitz constraint qualification and Karush–Kuhn–Tucker conditions in nonsmooth semi-infinite multiobjective programming

On approximate positively properly efficient solutions in nonsmooth semi-infinite multiobjective optimization problems with data uncertainty

“…For isolated efficient solutions and properly efficient solutions for multiobjective optimization problems, we refer to [13,14,15,16,17,18] and the references therein. In addition, optimality conditions and duality for isolated efficient solutions/properly efficient solutions of semi-infinite multiobjective optimization problems were studied in [19,20,21,22,23,24,25]. However, there are few results on isolated efficient solutions/properly efficient solutions for the semi-infinite multiobjective optimization problems with uncertainty data [26].…”

Second-order Optimality Conditions for Nonsmooth Multiobjective Fractional Optimization Problems

“…When the objective function in a multiobjective optimization problem is represented by fractional formulae, the problem is said to be multiobjective fractional optimization problem. Recently, optimality conditions and dual theorems of multiobjective fractional optimization problems are popular in the field of optimization theories, see [4][5][6][7][8][9][10][11][12][13]. Ojha [4] considered a pair of second-order symmetric duals in the context of nondifferentiable multiobjective fractional programming problems.…”

“…Kim [8] established necessary and sufficient optimality conditions and duality results for the weakly efficient solution of nondifferentiable multiobjective fractional programming problems. Khanh and Tung [9] discussed dual Karush-Kuhn-Tucker necessary optimality conditions for a local Borwein-proper solution for nonsmooth semi-infinite multiobjective fractional problem and for a local isolated solution for semi-infinite minimax fractional problem, by using the notion of Michel-Penot subdifferentials with local Lipschitz, MP-regular, and directional differentiable data. Su and Hang [10] established optimality and duality for a local weak minimizer and a weak minimizer of nonsmooth general multiobjective fractional programming problem based on contingent derivatives with stable mappings.…”