An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints

Le Thi Khanh Hien () and Dimitri Papadimitriou
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Le Thi Khanh Hien: Huawei Belgium Research Center

Journal of Global Optimization, 2024, vol. 89, issue 4, No 4, 927-948

Abstract: Abstract In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with nonlinear coupling constraints. Distinctive features of our proposed method, when compared with other alternating direction methods of multipliers for solving non-convex problems with nonlinear coupling constraints, include: (i) we apply the inertial technique to the update of primal variables and (ii) we apply a non-standard update rule for the multiplier by scaling the multiplier by a factor before moving along the ascent direction where a relaxation parameter is allowed. Subsequential convergence and global convergence are presented for the proposed algorithm.

Keywords: Alternating direction methods of multipliers; Nonlinear coupling constraints; Logistic matrix factorization; Multiblock nonconvex optimization; Majorization minimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01382-4

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