Aggregation and discretization in multistage stochastic programming

• 成果类型: Article
• 署名作者: Kuhn, Daniel
• 署名单位: University of St Gallen
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0048-6
• 发表日期: 2008
• 页码: 61-94
• 关键词: scenario reduction; bounds; optimization; expectation; generation; trees

摘要

Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.