A strong dual for conic mixed-integer programs

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

doi:10.1137/110840868

A strong dual for conic mixed-integer programs

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

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

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 language	English
Pages (from-to)	1136-1150
Number of pages	15
Journal	SIAM Journal on Optimization
Volume	22
Issue number	3
DOIs	https://doi.org/10.1137/110840868
State	Published - 2012
Externally published	Yes

Keywords

Conic programming
Cutting planes
Duality
Mixed-integer nonlinear programming

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AU - Dey, Santanu S.

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AB - 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.

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A strong dual for conic mixed-integer programs

Abstract

Keywords

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