On an Extension of a Spare Regularization Model

Abdellatif Moudafi ()
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Abdellatif Moudafi: CNRS-L.I.S UMR 7296, Aix Marseille Université, Campus Universitaire de Saint-Jérôme, 13397 Marseille, France

Mathematics, 2023, vol. 11, issue 20, 1-12

Abstract: In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment.

Keywords: minimization; feasibility; l 0 -norm; Moreau envelope; fixed-point algorithm; forward–backward iterations; proximity mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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