An Optimal ADMM for Unilateral Obstacle Problems

被引:0
|
作者
Zhang, Shougui [1 ]
Cui, Xiyong [2 ]
Xiong, Guihua [1 ]
Ran, Ruisheng [3 ]
机构
[1] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
[2] CISDI Informat Technol Co Ltd, Chongqing 401120, Peoples R China
[3] Chongqing Normal Univ, Sch Comp & Informat Sci, Chongqing 401331, Peoples R China
关键词
unilateral obstacle problem; finite difference; ADMM; augmented Lagrangian; ALTERNATING DIRECTION METHOD; LINEAR COMPLEMENTARITY-PROBLEMS; SELF-ADAPTIVE PROJECTION; CONTACT PROBLEMS; MULTIPLIERS; ALGORITHM;
D O I
10.3390/math12121901
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页数:16
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