不确定信息下凸优化问题的鲁棒解刻划

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 257-264.

不确定信息下凸优化问题的鲁棒解刻划

孙祥凯

重庆工商大学数学与统计学院重庆 400067

收稿日期:2016-05-17 修回日期:2016-10-08 出版日期:2017-04-26 发布日期:2017-04-26
作者简介:孙祥凯,sxkcqu@163.com
基金资助:
国家自然科学基金（11301570，11401058，11471059）、重庆高校创新团队建设计划资助项目（CXTDX201601026）、重庆市基础与前沿研究计划项目（cstc2015jcyjA00002，cstc2016jcyjA0219）和重庆市教委研究项目（KJ1500626）

Characterizations of Robust Solution for Convex Optimization Problems with Data Uncertainty

Sun Xiangkai

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2016-05-17 Revised:2016-10-08 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11301570, 11401058, 11471059), the Program for University Innovation Team of Chongqing (CXTDX201601026), the Basic and Advanced Research Project of CQ CSTC (cstc2015jcyjA00002, cstc2016jcyjA0219) and the Education Committee Project Research Foundation of Chongqing (KJ1500626)

摘要/Abstract

摘要： 该文旨在研究一类不确定性凸优化问题的鲁棒最优解.借助次微分的性质，首先引入了一类鲁棒型次微分约束品性.随后借助此约束品性，刻划了该不确定性凸优化问题的鲁棒最优解.最后建立了该不确定凸优化问题与其对偶问题之间的Wolfe型鲁棒对偶性.

关键词: 鲁棒解, 次微分, 不确定凸优化

Abstract: In this paper,we consider robust efficient solutions for a convex optimization problem in the face of data uncertainty. By using the properties of the subdifferential,we first introduce a robust-type subdifferential constraint qualification, and then obtain some completely characterizations of the robust efficient solution of this uncertain convex optimization problem. By using the robust-type subdifferential constraint qualification, we also characterize Wolfe type robust duality for the uncertain convex optimization problem and its uncertain dual problem.

Key words: Robust solutions, Subdifferential, Uncertain convex optimization

中图分类号:

O221.2

孙祥凯. 不确定信息下凸优化问题的鲁棒解刻划[J]. 数学物理学报, 2017, 37(2): 257-264.

Sun Xiangkai. Characterizations of Robust Solution for Convex Optimization Problems with Data Uncertainty[J]. Acta mathematica scientia,Series A, 2017, 37(2): 257-264.

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