弱凸向量优化问题的最优性条件

2013-12-03王彩玲高慧岩

吉林大学学报（理学版） 2013年2期

关键词：最优性吉林大学向量

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}.

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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