Stochastic programming approach to optimization under uncertainty

• 成果类型: Article; Proceedings Paper
• 署名作者: Shapiro, Alexander
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0090-4
• 发表日期: 2008
• 页码: 183-220
• 关键词: epi-convergent discretizations; average approximation method; mathematical programs; Risk measures; coherent; regularization; complexity

摘要

In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.