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Duality for quasiconvex minimization over closed convex cones

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A Correction to this article was published on 16 July 2021

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Abstract

We establish a general duality theorem in a generalized conjugacy framework, which generalizes a classical result on the minimization of a convex function over a closed convex cone. Our theorem yields two quasiconvex duality schemes; one of them is of the surrogate duality type and is applicable to problems having an evenly quasiconvex objective function, whereas the other one is applicable to problems with Lipschitz quasiconvex objective functions and yields duals whose objective functions do not involve any surrogate constraint.

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Acknowledgements

Juan Enrique Martínez-Legaz gratefully acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities, through Grant PGC2018-097960-B-C21 and the Severo Ochoa Program for Centers of Excellence in R&D (CEX2019-000915-S). He is affiliated with MOVE (Markets, Organizations and Votes in Economics). Wilfredo Sosa was supported in part by Fundação de Apoio à Pesquisa do Distrito Federal (FAP-DF), through Grants 0193.001695/2017 and PDE 05/2018. This research was carried out during the state of alert in Catalonia, when he was visiting the Centre de Recerca Matem àtica (CRM) in the framework of the 2020 Research in Pairs program. The CRM is a paradise for research, he appreciates the hospitality and all the support received from the CRM. We are grateful to two anonymous reviewers, whose careful reading of the manuscript and useful remarks have helped us to correct and improve the presentation.

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Authors and Affiliations

  1. Department d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona, Bellaterra, Spain

    Juan Enrique Martínez-Legaz

  2. Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain

    Juan Enrique Martínez-Legaz

  3. Graduate School in Economics, Catholic University of Brasilia, SGAN 916 - Modulo B, 70790-000, Brasilia-DF, Brazil

    Wilfredo Sosa

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  1. Juan Enrique Martínez-Legaz
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  2. Wilfredo Sosa
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Correspondence to Juan Enrique Martínez-Legaz.

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Martínez-Legaz, J.E., Sosa, W. Duality for quasiconvex minimization over closed convex cones. Optim Lett 16, 1337–1352 (2022). https://doi.org/10.1007/s11590-021-01766-5

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