On the existence of duality gaps for mixed integer programming

Authors:
Yoshihiro Tanaka
Affiliations:
Graduate School of Economics and Business Administration, Hokkaido University, Sapporo, Japan
Venue:
International Journal of Systems Science
Year:
2005

Citing 6
Cited 0

Integer and combinatorial optimization

Integer and combinatorial optimization
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Discrete optimization
A result in surrogate duality for certain integer programming problems

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Optimization by Vector Space Methods
Zero duality gap in integer programming: P-norm surrogate constraint method

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Abstract

Only a few theoretical studies of surrogate duality have been carried out since Greenberg and Pierskalla's comprehensive work. Recently, Ram and Karwan examined surrogate duality, and exemplified the existence of surrogate duality gaps for a class of mixed integer programming problems. In this paper, we show that the surrogate duality gaps may exist even for integer programming problems and present necessary sufficient conditions for surrogate (or Langrangion) duality gaps to occur. Then, we extend the results for a class of mixed integer programming problems.