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Duality for convex infinite optimization on linear spaces

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A Correction to this article was published on 30 March 2022

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Abstract

This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.

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Acknowledgements

This research was partially supported by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI), and European Regional Development Fund (ERDF), Project PGC2018-097960-B-C22.

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  1. Department of Mathematics, University of Alicante, Alicante, Spain

    M. A. Goberna

  2. Avignon University, LMA EA 2151, Avignon, France

    M. Volle

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  1. M. A. Goberna
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  2. M. Volle
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Correspondence to M. A. Goberna.

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Goberna, M.A., Volle, M. Duality for convex infinite optimization on linear spaces. Optim Lett 16, 2501–2510 (2022). https://doi.org/10.1007/s11590-022-01865-x

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