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

• Published in: Journal of global optimization Vol. 89; no. 4; pp. 927 - 948
• Main Authors: Hien, Le Thi Khanh, Papadimitriou, Dimitri
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer; Springer Nature B.V
• Subjects: Algorithms; Comparative analysis; Computer Science; Constraints; Convergence; Coupling; Mathematics; Mathematics and Statistics; Methods; Multipliers; Operations Research/Decision Theory; Optimization; Real Functions; Logistic matrix factorization; Multiblock nonconvex optimization; Alternating direction methods of multipliers; Nonlinear coupling constraints; Majorization minimization
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-024-01382-4

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.