A convex combined symmetric alternating direction method of multipliers for separable optimization

Xiaoquan Wang (), Hu Shao () and Ting Wu ()
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Xiaoquan Wang: China University of Mining and Technology
Hu Shao: China University of Mining and Technology
Ting Wu: Nanjing University

Computational Optimization and Applications, 2025, vol. 90, issue 3, No 8, 839-880

Abstract: Abstract The Alternating Direction Method of Multipliers (ADMM) is a powerful first-order method used in many practical separable optimization problems. In this paper, we propose a new variant of the symmetric ADMM, called the Convex Combined Symmetric ADMM (CcS-ADMM), by integrating a convex combination technique. CcS-ADMM retains all the favorable features of ADMM, including the ability to take full advantage of problem structures and global convergence under relaxed parameter conditions. Furthermore, using the moderate assumptions and primal-dual gap, we analyze the convergence and the O(1/N) ergodic convergence rate of the algorithm with convex setting. Additionally, we propose the convergence of the CcS-ADMM with nonconvex setting in Euclidean space under so called Kurdyka–Lojasiewicz property and some widely used assumptions, and we establish the pointwise iteration-complexity of CcS-ADMM with respect to the augmented Lagrangian function and the primal-dual residuals. Finally, we present the results from preliminary numerical experiments to demonstrate the performance of the proposed algorithms.

Keywords: Separable optimization problem with constraints; Alternating direction method of multipliers; Convex combination; Primal-dual gap; Convergence analysis; Nonconvex setting (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00647-2

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