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.
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页数:16
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