A strong dual for conic mixed-integer programs

Diego A. Morán R., Santanu S. Dey, Juan Pablo Vielma

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [M. Güzelsoy and T. K. Ralphs, Int. J. Oper. Res. (Taichung), 4 (2007), pp. 118-137], [G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley-Interscience, New York, 1988]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we show that strong duality holds.

Original languageEnglish
Pages (from-to)1136-1150
Number of pages15
JournalSIAM Journal on Optimization
Issue number3
StatePublished - 2012
Externally publishedYes


  • Conic programming
  • Cutting planes
  • Duality
  • Mixed-integer nonlinear programming


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