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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.22 no.1 Temuco Apr. 2020

http://dx.doi.org/10.4067/S0719-06462020000100137 

Articles

Level sets regularization with application to optimization problems

Moussa Barro1 

Sado Traore2 

1Université Nazi BONI, Burkina Faso. mousbarro@yahoo.fr

2Université Nazi BONI, Burkina Faso. traore.sado@yahoo.fr

Abstract

Given a coupling function c and a non empty subset of R, we define a closure operator. We are interested in extended real-valued functions whose sub-level sets are closed for this operator. Since this class of functions is closed under pointwise suprema, we introduce a regularization for extended real-valued functions. By decomposition of the closure operator using polarity scheme, we recover the regularization by bi-conjugation. We apply our results to derive a strong duality for a minimization problem.

Keywords and Phrases: Duality; regularization; level sets; c-elementary functions; polarity; conjugacy

Resumen

Dada una función de acoplamiento c y un subconjunto no vacío de R, definimos un operador clausura. Estamos interesados en funciones extendidas a valores reales cuyos conjuntos de sub-nivel son cerrados para este operador. Dado que esta clase de funciones es cerrada bajo supremos puntuales, introducimos una regularización para funciones extendidas a valores reales. Gracias a la descomposición del operador clausura usando el esquema de polaridad, recuperamos la regularización por bi-conjugación. Aplicamos nuestros resultados para derivar una dualidad fuerte para un problema de minimización.

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Acknowledgements

The authors are grateful to the anonymous referees and the editor for their constructive comments which have contributed to the final presentation of the paper.

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