A Relative Inexact Proximal Gradient Method with an Explicit Linesearch

Yunier Bello-Cruz (), Max L. N. Gonçalves (), Jefferson G. Melo () and Cassandra Mohr ()
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Yunier Bello-Cruz: Northern Illinois University
Max L. N. Gonçalves: Federal University of Goias
Jefferson G. Melo: Federal University of Goias
Cassandra Mohr: Northern Illinois University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 1, No 9, 32 pages

Abstract: Abstract This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a non-differentiable convex function. We introduce an explicit line search applied specifically to the differentiable component of the objective function, requiring only a relative inexact solution of the proximal subproblem per iteration. We prove the convergence of the sequence generated by our scheme and establish its iteration complexity, considering both the functional values and a residual associated with first-order stationary solutions. Additionally, we provide numerical experiments to illustrate the practical efficacy of our method.

Keywords: Linesearch; Iteration complexity; Nonsmooth and convex optimization problem; Proximal gradient method; Relative error rule; 65K05; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02684-7

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