Minimizing buffered probability of exceedance by progressive hedging
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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.
KeywordsConvex stochastic programming problems Probability of failure Probability of exceedance Buffered probability of failure Buffered probability of exceedance Quantiles Superquantiles Conditional value-at-risk Progressive hedging algorithm
Mathematics Subject Classification90C15
This research was sponsored for both authors by DARPA EQUiPS Grant SNL 014150709. The authors are grateful also to Dr. Viktor Kuzmeno for help with conducting the numerical case study.
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