Level sets regularization with application to optimization problems
Author
Barro, Moussa
Traoré, Sado
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/226010.4067/S0719-06462020000100137
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.