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Ambiguous Risk Constraints with Moment and Unimodality Information

Bowen Li(libowen***at***umich.edu)
Ruiwei Jiang(ruiwei***at***umich.edu)
Johanna L. Mathieu(jlmath***at***umich.edu)

Abstract: Optimization problems face random constraint violations when uncertainty arises in constraint parameters. Effective ways of controlling such violations include risk constraints, e.g., chance constraints and conditional Value-at-Risk (CVaR) constraints. This paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous. In particular, we assume that the distributional information consists of the first two moments of the uncertainty and a generalized notion of unimodality. We find that the ambiguous risk constraints in this setting can be recast as a set of second-order cone (SOC) constraints. In order to facilitate the algorithmic implementation, we also derive efficient ways of finding violated SOC constraints. Finally, we demonstrate the theoretical results via a computational case study on power system operations.

Keywords: ambiguity, chance constraints, conditional Value-at-Risk, second-order cone representation, separation, golden section search

Category 1: Stochastic Programming

Category 2: Robust Optimization

Citation: University of Michigan, 2016.

Download: [PDF]

Entry Submitted: 09/14/2016
Entry Accepted: 09/18/2016
Entry Last Modified: 09/14/2016

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