Ambiguous risk constraints with moment and unimodality information

Bowen Li, Ruiwei Jiang, Johanna L. Mathieu

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


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 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 computational case studies on power system operations.

Original languageEnglish (US)
Pages (from-to)151-192
Number of pages42
JournalMathematical Programming
Issue number1-2
StatePublished - Jan 23 2019


  • Ambiguity
  • Chance constraints
  • Conditional Value-at-Risk
  • Golden section search
  • Second-order cone representation
  • Separation

ASJC Scopus subject areas

  • Software
  • General Mathematics


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