一类非光滑优化问题解集的性质

运筹学学报 ›› 2012, Vol. 16 ›› Issue (3): 109-118.

一类非光滑优化问题解集的性质

赵克全¹, 杨新民²

1. 内蒙古大学数学科学学院 2. 重庆师范大学数学学院

收稿日期:2009-05-31 修回日期:2012-04-28 出版日期:2012-09-15 发布日期:2012-09-18
通讯作者: 赵克全 E-mail:kequanz@163.com

Characterizations of the solution set for a class of nonsmooth optimization problems

ZHAO Kequan¹, YANG Xinmin²

1. College of Mathematics Science, Inner Mongolia University 2. College of Mathematics Science, Chongqing Normal University

Received:2009-05-31 Revised:2012-04-28 Online:2012-09-15 Published:2012-09-18
Contact: Ke-Quan Zhao E-mail:kequanz@163.com
Supported by:
National Natural Science Foundation of China (Nos. 11126348, 11001289), Natural Science Foundation Project of Chongqing (No. 2011BA0030), Special Fund of Chongqing Key Laboratory (Nos. CSTC, 2011KLORSE02) and the Education Committee Research Foundation of Chongqing (No. KJ110625).

摘要/Abstract

摘要： 研究了一类带不等式约束的非光滑优化问题，利用Clarke 次微分和Lagrange 乘子研究该类问题的解集的一些性质，给出了一个例子解释主要结果. 主要结论是对最近一些文献中相应结果的改进与推广.

关键词: 非光滑优化, 解集, 伪不变凸性, Lagrange 乘子, Clarke 次微分

Abstract: In this paper, a class of nonsmooth optimization problems with inequality constraints is considered. Characterizations of the solution set are obtained in terms of Clarke subdifferentials and Lagrange multipliers. An example is given to illustrate the main results. The resluts improve and extend some previously known results.

Key words: nonsmooth optimization, solution set, pseudoinvexity, Lagrange multipliers, Clarke subdifferentials

中图分类号:

90C26
90C30

赵克全,杨新民. 一类非光滑优化问题解集的性质[J]. 运筹学学报, 2012, 16(3): 109-118.

ZHAO Kequan, YANG Xinmin. Characterizations of the solution set for a class of nonsmooth optimization problems[J]. Operations Research Transactions, 2012, 16(3): 109-118.

参考文献

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