Level sets regularization with application to optimization problems

  • 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.
Keywords: Duality, regularization, level sets, c-elementary functions, polarity, conjugacy

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.

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Published
2020-04-18
How to Cite
Barro, M., & Traoré, S. (2020). Level sets regularization with application to optimization problems. CUBO, A Mathematical Journal, 22(1), 137–154. https://doi.org/10.4067/S0719-06462020000100137