This paper considers a multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. By developing the idea of using the information zone and adaptive regime proposed in [J. Bolte, S. Sabach and M. Teboulle, Nonconvex Lagrangian-based optimization: Monitoring schemes and global convergence, Mathematics of Operations Research, 43: 1210--1232, 2018], we propose a multiblock alternating direction method of multipliers for solving this problem. We specify the update of the primal variables by employing a majorization minimization procedure in each block update. An independent convergence analysis is conducted to prove the subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.

翻译：本文考虑了非线性联结制约下的一个多块非单体非相通非相通优化问题。通过发展使用[J. Bolte、S. Sabach和M. Tebulle,Nonconvex Lagrangian的优化:监测计划和全球趋同,行动研究数学,43:1210-1232,2018]所提议的信息区和适应制度的想法,我们提出了解决该问题的多块交替乘数方向方法。我们通过在每块更新中采用主要最小化程序,具体说明了原始变量的更新情况。进行了独立的趋同分析,以证明生成的序列随后与全球趋同到拉格朗江增强的临界点。我们还确定了变相的复杂性,并为拟议的算法提供了初步的数字结果。