弱凸向量优化问题的最优性条件

王彩玲, 高慧岩

(1. 吉林大学 数学学院, 长春 130012; 2. 北京中科金财科技股份有限公司, 北京 100083)

文献[1-6]利用抽象次微分对单目标规划问题进行了研究. 本文利用抽象次微分给出目标函数为弱凸函数的向量优化问题的最优性条件, 推广了文献[1-6]的结果.

1 抽象凸函数的概念

考虑如下多目标规划问题：

∀x∈Rn}.

∀x∈Rn}.

2 最优性条件

证明： 首先, 证明

其次, 证明

由于

(1)

又因为

(2)

(3)

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