Forward-Primal-Dual-Half-Forward Algorithm for Splitting Four Operators

Fernando Roldán ()
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Fernando Roldán: Universidad de Concepción

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 1, No 11, 26 pages

Abstract: Abstract In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitz operator, a cocoercive operator, and a linear composite term. In the case where the Lipschitz operator is absent, our method reduces to the Condat-Vũ algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. Therefore, our algorithm can be seen as a combination of Condat-Vũ and FBHF. Moreover, we propose extensions and applications of our method in multivariate monotone inclusions and saddle point problems. Finally, we present a numerical experiment on image deblurring problems.

Keywords: Operator splitting; Monotone operators; Monotone inclusion; Convergence analysis; Convex optimization; 47H05; 65K05; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02560-w

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