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Higher-moment buffered probability

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A Correction to this article was published on 28 March 2019

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Abstract

In stochastic optimization, probabilities naturally arise as cost functionals and chance constraints. Unfortunately, these functions are difficult to handle both theoretically and computationally. The buffered probability of failure and its subsequent extensions were developed as numerically tractable, conservative surrogates for probabilistic computations. In this manuscript, we introduce the higher-moment buffered probability. Whereas the buffered probability is defined using the conditional value-at-risk, the higher-moment buffered probability is defined using higher-moment coherent risk measures. In this way, the higher-moment buffered probability encodes information about the magnitude of tail moments, not simply the tail average. We prove that the higher-moment buffered probability is closed, monotonic, quasi-convex and can be computed by solving a smooth one-dimensional convex optimization problem. These properties enable smooth reformulations of both higher-moment buffered probability cost functionals and constraints.

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  • 28 March 2019

    The original version of this article unfortunately contained a mistake. The copyright line was incorrect.

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Acknowledgements

The author gratefully acknowledges the comments and suggestions from the reviewers. Their comments helped to simplify the original results in Sect. 3. This research was sponsored by DARPA EQUiPS Grant SNL 014150709

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  1. Optimization and Uncertainty Quantification, Sandia National Laboratories, P.O. Box 5800, MS-1320, Albuquerque, NM, 87185-1320, USA

    D. P. Kouri

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Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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Kouri, D.P. Higher-moment buffered probability. Optim Lett 13, 1223–1237 (2019). https://doi.org/10.1007/s11590-018-1359-2

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