Higher-moment buffered probability

Journal Article · Fri Feb 22 00:00:00 EST 2019 · Optimization Letters

DOI:https://doi.org/10.1007/s11590-018-1359-2· OSTI ID:1497635

Kouri, D. P. ^[1]

---

1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: DARPA; USDOE
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1497635
• Report Number(s): SAND--2019-2008J; 672842
• Journal Information: Optimization Letters, Journal Name: Optimization Letters Journal Issue: 6 Vol. 13; ISSN 1862-4472
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Chance constraints
Conditional value-at-risk
Risk measures
Stochastic programming