On Valid Inequalities for Mixed Integer p-Order Cone Programming

Alexander Vinel, Pavlo Krokhmal

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We discuss two families of valid inequalities for linear mixed integer programming problems with cone constraints of arbitrary order, which arise in the context of stochastic optimization with downside risk measures. In particular, we extend the results of Atamtürk and Narayanan (Math. Program., 122:1-20, 2010, Math. Program., 126:351-363, 2011), who developed mixed integer rounding cuts and lifted cuts for mixed integer programming problems with second-order cone constraints. Numerical experiments conducted on randomly generated problems and portfolio optimization problems with historical data demonstrate the effectiveness of the proposed methods.

Original languageEnglish (US)
Pages (from-to)439-456
Number of pages18
JournalJournal of Optimization Theory and Applications
Issue number2
StatePublished - Feb 2014


  • Mixed integer p-order cone programming
  • Nonlinear cuts
  • Risk measures
  • Stochastic optimization
  • Valid inequalities

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics


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