Consensus-based Distributed Augmented Lagrangian Method for Nonconvex Optimization with Coupled Constraints
Yanxu Su · 2022
Abstract: In this paper, we study the nonconvex optimization problems with consideration of globally coupled constraints. The constrained optimization problem is converted into an augmented Lagrangian function, and a distributed primal-dual algorithm is exploited in the context of finite-time consensus for solving such a problem. Particularly, we do not require the globally coupled constraints to be separable. Instead, we introduce some local variables for estimating the constraint violations. Under some mild assumptions in the research of nonconvex optimization, we prove the convergence of the presented algorithm to a KKT point of the problem. The numerical experiment verifies the correctness and the effectiveness of the theoretical results.