Volume 40 Issue 5
May. 2023
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JOURNAL OF MECHANICAL ENGINEERING  > 2023  >  44(5): 595-604.
ZHANG Linsen, CHENG Lan, ZHANG Shougui. An Alternating Direction Multiplier Method for 4th-Order Variational Inequalities With Curvature Obstacle[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 595-604. doi: 10.21656/1000-0887.430243
Citation: ZHANG Linsen, CHENG Lan, ZHANG Shougui. An Alternating Direction Multiplier Method for 4th-Order Variational Inequalities With Curvature Obstacle[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 595-604. doi: 10.21656/1000-0887.430243
shu

An Alternating Direction Multiplier Method for 4th-Order Variational Inequalities With Curvature Obstacle

doi: 10.21656/1000-0887.430243

  • School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Funds:

The National Natural Science Foundation of China(11971085)

  • Received Date: 23 Jul 2022
  • Rev Recd Date: 19 Sep 2022
  • Issue Publish Date: 31 May 2023
    Abstract
  • A self-adaptive alternating direction method of multipliers was proposed for the approximation solution of variational inequalities with biharmonic operators and curvature obstacle. An augmented Lagrange functional was introduced with an auxiliary variable to express the curvature function, and a constrained minimization problem equivalent to a saddle-point one was deduced. Then the alternating direction method of multipliers was applied to solve the saddle-point problem. By means of the balance principle and iterative functions, a self-adaptive rule was obtained to adjust the penalty parameter automatically, and improve the computation efficiency. The convergence of this method was proved and the penalty parameter approximation was given in detail with the iterative functions. The numerical results illustrate the effectiveness of the proposed method.

     

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