On Valid Inequalities for Mixed Integer p-Order Cone Programming

Alexander Vinel, Pavlo Krokhmal

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

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
Volume160
Issue number2
DOIs
StatePublished - Feb 2014
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

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

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