A preliminary set of applications leading to stochastic semidefinite programs and chance-constrained semidefinite programs

作     者：Zhu, Yuntao Ariyawansa, K. A. 

作者机构：Washington State Univ Dept Math Pullman WA 99164 USA Arizona State Univ Div Math & Nat Sci Phoenix AZ 85069 USA 

出 版 物：《APPLIED MATHEMATICAL MODELLING》 (应用数学模型)

年 卷 期：2011年第35卷第5期

页      面：2425-2442页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：ASU West MGIA US Army Research Office [DAAD 19-00-1-0465, W911NF-08-1-0530] 

主　　题：Linear programming Stochastic programming Semidefinite programming Chance-constraints Optimization models 

摘      要：Ariyawansa and Zhu have recently introduced (two-stage) stochastic semidefinite programs (with recourse) (SSDPs) [1] and chance-constrained semidefinite programs (CCSDPs) [2] as paradigms for dealing with uncertainty in applications leading to semidefinite programs. Semidefinite programs have been the subject of intense research during the past 15 years, and one of the reasons for this research activity is the novelty and variety of applications of semidefinite programs. This research activity has produced, among other things, efficient interior point algorithms for semidefinite programs. Semidefinite programs however are defined using deterministic data while uncertainty is naturally present in applications. The definitions of SSDPs and CCSDPs in [1.2] were formulated with the expectation that they would enhance optimization modeling in applications that lead to semidefinite programs by providing ways to handle uncertainty in data. In this paper, we present results of our attempts to create SSDP and CCSDP models in four such applications. Our results are promising and we hope that the applications presented in this paper would encourage researchers to consider SSDP and CCSDP as new paradigms for stochastic optimization when they formulate optimization models. (C) 2010 Elsevier Inc. All rights reserved.