Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach

• 成果类型: Article
• 署名作者: Hong, L. Jeff; Yang, Yi; Zhang, Liwei
• 署名单位: Hong Kong University of Science & Technology; University of California System; University of California Irvine; Dalian University of Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1100.0910
• 发表日期: 2011
• 页码: 617-630
• 关键词: probabilistic constraints; linear-programs; optimization; SENSITIVITIES; DESIGN; price; RISK

摘要

When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP), which requires that all constraints be satisfied simultaneously with a given large probability. In this paper, we propose to solve the JCCP by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime. Furthermore, we propose to use a gradient-based Monte Carlo method to solve the sequence of convex approximations.