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运筹学学报 >

2017 , Vol. 21 >Issue 2: 24 - 30

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2017.02.003

运筹学

一类带概率互补约束的随机优化问题的最优性条件

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  • 1. 四川大学数学学院, 成都  610064; 2. 重庆师范大学数学科学学院, 重庆 400047

收稿日期: 2017-04-10

  网络出版日期: 2017-06-15

基金资助

国家自然科学基金(No. 11431004)

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Optimality conditions for a class of stochastic optimization problems with probabilistic complementarity constraints

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  • 1. Collage of Mathematics, Sichuan University, Chengdu 610064, China; 2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China

Received date: 2017-04-10

  Online published: 2017-06-15

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摘要

主要讨论了一类带概率互补约束的随机优化问题的最优性条件. 首先利用一类非线性互补(NCP)函数将概率互补约束转化成为一个通常的概率约束. 然后, 利用概率约束的相关理论结果, 将其等价地转化成一个带不等式约束的优化问题. 最后给出了这类问题的弱驻点和最优解的最优性条件.

关键词： 概率互补约束; NCP 函数; alpha-凹函数; 最优性条件

本文引用格式

陈林, 杨新民 . 一类带概率互补约束的随机优化问题的最优性条件[J]. 运筹学学报, 2017 , 21(2) : 24 -30 . DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.003

Abstract

In this paper, we focus on the optimality conditions for a class of stochastic optimization problem with probabilistic complementarity constraints. By using a kind of nonlinear complementarity (NCP) function,  we transform the probabilistic complementary constraint into a chance constraint. By using the theories in chance constraint,  we obtain an optimization problem with inequality constraint and  then, optimality conditions for weak stationary points and the optimal solutions are given.

Key words： probabilistic complementarity constraints; NCP function; alpha-concave function; optimality conditions

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