An Improvement of the Alternating Direction Method of Multipliers to Solve the Convex Optimization Problem

Jingjing Peng (), Zhijie Wang, Siting Yu and Zengao Tang
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Jingjing Peng: College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Zhijie Wang: College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Siting Yu: College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Zengao Tang: College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China

Mathematics, 2025, vol. 13, issue 5, 1-19

Abstract: The alternating direction method is one of the attractive approaches for solving convex optimization problems with linear constraints and separable objective functions. Experience with applications has shown that the number of iterations depends significantly on the penalty parameter for the linear constraint. The penalty parameters in the classical alternating direction method are a constant. In this paper, an improved alternating direction method is proposed, which not only adaptively adjusts the penalty parameters per iteration based on the iteration message but also adds relaxation factors to the Lagrange multiplier update steps. Preliminary numerical experiments show that the technique of adaptive adjusting of the penalty parameters per iteration and attaching relaxation factors in the Lagrange multiplier updating steps are effective in practical applications.

Keywords: convex optimization; alternating direction method of multipliers; symmetric alternating direction method of multipliers; global convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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