一类非光滑多目标分式优化问题的二阶最优性条件

Second-Order Optimality Conditions for a Nonsmooth Multiobjective Fractional Optimization Problem

本文研究一类带不等式约束和退化等式约束的多目标分式优化问题(FOP)存在局部弱Pareto最优解、二阶严格局部Pareto最优解的二阶必要条件,建立了(FOP)关于局部弱Pareto最优解的对偶Fritz-John型二阶必要条件,通过约束条件,将Fritz-John型必要条件变为Kuhn-Tucher型,并举例说明主要定理的适用性。本文主要工作旨在将多目标整式优化问题二阶最优性条件的研究推广到多目标分式优化问题。

In this paper, we consider a class of multiobjective fractional optimization problems (FOP) with in-equality and degenerate equality constraints. Some second-order optimality conditions for a local weak Pareto minimum and a strict local Pareto minimum of order two are given. Then we establish Fritz-John type necessary conditions for local weak Pareto minimum to problem (FOP), meanwhile, by introducing constraint qualifications, we prove that the Fritz-John type necessary conditions be-come the Kuhn-Tucker type. The applicability of our conclusions is illustrated with some examples. The main purpose of this paper is to extend the study of second-order optimality conditions for multiobjective integer optimization problems to multiobjective fractional optimization problems.