Quadratic two-stage stochastic optimization with coherent measures of risk

• 成果类型: Article
• 署名作者: Sun, Jie; Liao, Li-Zhi; Rodrigues, Brian
• 署名单位: Curtin University; Curtin University; National University of Singapore; Hong Kong Baptist University; Singapore Management University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1131-x
• 发表日期: 2018
• 页码: 599-613
• 关键词: robust convex-optimization; linear-programs; uncertainty

摘要

A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second stage objective functions are convex linear-quadratic. It is shown that under a standard set of regularity assumptions, this two-stage quadratic stochastic optimization problem with measures of risk is equivalent to a conic optimization problem that can be solved in polynomial time.