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<p>In this paper, we investigate necessary optimality conditions for isolated efficient solutions and positively properly efficient solutions of nonsmooth fractional multiobjective optimization problems involving equality and inequality constraints. Besides, sufficient optimality conditions for the existence of isolated efficient solutions and positively properly efficient solutions also are discussed under the assumptions of convexity or generalized convexity. Furthermore, we also investigate types of Mond–Weir multiobjective dual problem for the primal problem under suitable assumptions on the generalized convexity. We also introduce applications to nonsmooth minimax programming problems. The obtained results improve or include some recent known ones. Some examples are given to illustrate the obtained results.</p>

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On isolated and proper efficiencies in fractional multiobjective optimization problems involving equality and inequality constraints

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Thanh-Hung Pham

摘要

In this paper, we investigate necessary optimality conditions for isolated efficient solutions and positively properly efficient solutions of nonsmooth fractional multiobjective optimization problems involving equality and inequality constraints. Besides, sufficient optimality conditions for the existence of isolated efficient solutions and positively properly efficient solutions also are discussed under the assumptions of convexity or generalized convexity. Furthermore, we also investigate types of Mond–Weir multiobjective dual problem for the primal problem under suitable assumptions on the generalized convexity. We also introduce applications to nonsmooth minimax programming problems. The obtained results improve or include some recent known ones. Some examples are given to illustrate the obtained results.