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Necessary and Sufficient Constraint Qualification for Surrogate Duality

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Abstract

In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient constraint qualification for surrogate duality has not been proposed yet. In this paper, we propose necessary and sufficient constraint qualifications for surrogate duality and surrogate min–max duality, which are closely related with ones for Lagrange duality.

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Authors and Affiliations

  1. Interdisciplinary Faculty of Science and Engineering, Shimane University, 1060, Nishikawatsu, Matsue, Shimane, 690-8504, Japan

    Satoshi Suzuki & Daishi Kuroiwa

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  1. Satoshi Suzuki
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  2. Daishi Kuroiwa
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Correspondence to Satoshi Suzuki.

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Communicated by Vaithilingam Jeyakumar.

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Suzuki, S., Kuroiwa, D. Necessary and Sufficient Constraint Qualification for Surrogate Duality. J Optim Theory Appl 152, 366–377 (2012). https://doi.org/10.1007/s10957-011-9893-4

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  • DOI: https://doi.org/10.1007/s10957-011-9893-4

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