Minimizing buffered probability of exceedance by progressive hedging

• 成果类型: Article
• 署名作者: Rockafellar, R. Tyrrell; Uryasev, Stan
• 署名单位: University of Washington; University of Washington Seattle; State University System of Florida; University of Florida
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01462-4
• 发表日期: 2020
• 页码: 453-472
• 关键词: risk; optimization; regression

摘要

Stochastic programming problems have for a long time been posed in terms of minimizing the expected value of a random variable influenced by decision variables, but alternative objectives can also be considered, such as minimizing a measure of risk. Here something different is introduced: minimizing the buffered probability of exceedance for a specified loss threshold. The buffered version of the traditional concept of probability of exceedance has recently been developed with many attractive properties that are conducive to successful optimization, in contrast to the usual concept, which is often posed simply as the probability of failure. The main contribution here is to demonstrate that in minimizing buffered probability of exceedance the underlying convexities in a stochastic programming problem can be maintained and the progressive hedging algorithm can be employed to compute a solution.