An Optimal ADMM for Unilateral Obstacle Problems

Shougui Zhang (), Xiyong Cui, Guihua Xiong and Ruisheng Ran
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Shougui Zhang: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
Xiyong Cui: CISDI Information Technology Co., Ltd., Chongqing 401120, China
Guihua Xiong: School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
Ruisheng Ran: School of Computer and Information Science, Chongqing Normal University, Chongqing 401331, China

Mathematics, 2024, vol. 12, issue 12, 1-16

Abstract: We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study.

Keywords: unilateral obstacle problem; finite difference; ADMM; augmented Lagrangian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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