Ambiguous Risk Constraints with Moment and Unimodality Information
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.
Entry Submitted: 09/14/2016
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