不确定信息下凸优化问题的鲁棒解刻划

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (2): 257-264.

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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)

Abstract

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

CLC Number:

O221.2

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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Characterizations of Robust Solution for Convex Optimization Problems with Data Uncertainty

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