Mixed integer programming with a class of nonlinear convex constraints

Alexander Vinel, Pavlo A. Krokhmal

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second- and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be generalized to the problems under consideration. Particularly, we consider a branch-and-bound method based on outer polyhedral approximations, lifted nonlinear cuts, and linear disjunctive cuts. Results of numerical experiments with discrete portfolio optimization models are presented.

Original languageEnglish (US)
Pages (from-to)66-86
Number of pages21
JournalDiscrete Optimization
StatePublished - May 1 2017
Externally publishedYes


  • Conic programming
  • Measures of risk
  • Mixed-integer nonlinear programming
  • Quasi-arithmetic average
  • Valid inequalities

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics


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