Level sets regularization with application to optimization problems

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DOI:

https://doi.org/10.4067/S0719-06462020000100137

Abstract

Given a coupling function \(c\) and a non empty subset of â„, 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

Duality , regularization , level sets , c-elementary functions , polarity , conjugacy
  • Moussa Barro Département de Mathématiques, UFR des Sciences et Techniques, Université Nazi BONI, Burkina Faso.
  • Sado Traoré Département de Mathématiques, UFR des Sciences et Techniques, Université Nazi BONI, Burkina Faso.
  • Pages: 137–154
  • Date Published: 2020-04-18
  • Vol. 22 No. 1 (2020)

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Published

2020-04-18

How to Cite

[1]
M. Barro and S. . Traoré, “Level sets regularization with application to optimization problems”, CUBO, vol. 22, no. 1, pp. 137–154, Apr. 2020.

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Vol. 22 No. 1 (2020)

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