ABSTRACT

The notions of higher-order Studniarski derivative and m-stable functions (m is a positive integer) are introduced for dealing with multiobjective semi-infinite programming problem with inequality constraints. In order to obtain results on necessary optimality conditions of higher order, we study two generalized Abadie constraint qualifications for these notions together with the existence results of Studniarski derivative of higher order. An application of these constraint qualifications for the Borwein properly efficient solution on weak and strong Karush–Kuhn–Tucker necessary optimality conditions via the higher-order Studniarski derivatives with m-stable functions is presented. A higher-order sufficient optimality condition which is very close to higher-order strong Karush–Kuhn–Tucker necessary conditions to such problem is provided as well. Several examples are also constructed to illustrate the main results of the paper.

摘要

引入高阶Studniarski导数和m -stable函数（m为正整数）的概念来处理具有不等式约束的多目标半无限规划问题。为了获得高阶必要最优性条件的结果，我们研究了这些概念的两个广义Abadie约束条件以及高阶Studniarski导数的存在性结果。通过具有m的高阶 Studniarski 导数将这些约束条件应用于弱和强 Karush-Kuhn-Tucker 必要最优性条件的 Borwein 适当有效解- 提供稳定的功能。还提供了一个与该问题的高阶强Karush-Kuhn-Tucker必要条件非常接近的高阶充分最优性条件。还构建了几个例子来说明本文的主要结果。