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Mathematics > Optimization and Control

arXiv:2212.12256 (math)
[Submitted on 23 Dec 2022]

Title:On a fixed-point continuation method for a convex optimization problem

Authors:Jean-Baptiste Fest, Tommi Heikkilä, Ignace Loris, Ségolène Martin, Luca Ratti, Simone Rebegoldi, Gesa Sarnighausen
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Abstract:We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a penalty parameter. This so-called fixed-point continuation method allows one to approximate the problem's trade-off curve, i.e. to compute the minimizers of the cost function for a whole range of values of the penalty parameter at once. The algorithm is shown to converge, and a rate of convergence of the cost function is also derived. Furthermore, it is shown that this method is related to iterative algorithms constructed on the basis of the $\epsilon$-subdifferential of the prox-simple term. Some numerical examples are provided.
Comments: 15 pages, 2 figures. Workshop on Advanced Techniques in Optimization for Machine learning and Imaging
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
Cite as: arXiv:2212.12256 [math.OC]
  (or arXiv:2212.12256v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2212.12256
Related DOI: https://doi.org/10.1007/978-981-97-6769-4_2

Submission history

From: Ignace Loris [view email]
[v1] Fri, 23 Dec 2022 11:08:01 UTC (127 KB)
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