What question did this study set out to answer?

To develop an efficient method for solving multi-block nonconvex optimization problems using a sequential complete inertial Bregman ADMM.

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April 15, 2026Open Access

A Sequential Complete Inertial Bregman Admm for Multi-Block Nonconvex Problems

Key Points

To develop an efficient method for solving multi-block nonconvex optimization problems using a sequential complete inertial Bregman ADMM.
Proposed the SCIB-ADMM algorithm integrating inertial strategy and Bregman distance.
Utilized two relaxation factors at each iteration.
Updated the Lagrange multiplier twice for improved convergence.
Achieved effective processing speed in numerical experiments.
Demonstrated convergence under appropriate assumptions.
Proven effectiveness on SCAD and robust PCA problems.

Abstract

In this paper, a sequential complete inertial Bregman alternating direction method of multipliers (SCIB-ADMM) is proposed for multi-block nonconvex problems. The iterative method is established by utilizing the inertial strategy and Bregman distance to enhance its processing speed and efficiency. At each iteration, the SCIB-ADMM method utilizes two different relaxation factors and updates the Lagrange multiplier twice. The convergence of the SCIB-ADMM can be established under appropriate assumptions. Moreover, numerical experiments are presented on smoothly clipped absolute deviation (SCAD) and robust principal component analysis (PCA) problems to show the effectiveness of the SCIB-ADMM method.

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