2021/10/24 by Weiwei Kong, Renato D. C. Monteiro, Kong, Weiwei +1 · 1 citation
Computer Science · Engineering · Mathematics · #65K10 #90C25 #90C26 #90C30 #90C60 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2110.12502
openalex publication_date 2021/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable. Each iteration of DP.ADMM consists of: (i) a sequence of partial proximal augmented Lagrangian (AL) updates, (ii) an under-relaxed Lagrange multiplier update, and (iii) a novel test to check whether the penalty parameter of the AL function should be updated. Under a basic Slater condition and some requirements related to the dampening factor and under-relaxation parameter, it is shown that DP.ADMM obtains a first-order stationary point of the constrained problem in \cal O(ε-3) iterations for a given numerical tolerance ε>0. One of the main novelties of the paper is that convergence of the method is obtained without requiring any rank assumptions on the constraint matrices.