An Alternating Direction Multiplier Method for <b>4</b>th-Order Variational Inequalities With Curvature Obstacle

ZHANG Linsen; CHENG Lan; ZHANG Shougui

doi:10.21656/1000-0887.430243

Volume 44 Issue 5

May 2023

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ZHANG Linsen, CHENG Lan, ZHANG Shougui. An Alternating Direction Multiplier Method for 4th-Order Variational Inequalities With Curvature Obstacle[J]. Applied Mathematics and Mechanics, 2023, 44(5): 595-604. doi: 10.21656/1000-0887.430243

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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

Received Date: 2022-07-23
Rev Recd Date: 2022-09-19
Publish Date: 2023-05-01

Abstract

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.
- 4th-order variational inequality,
- curvature obstacle,
- alternating direction multiplier method,
- self-adaptive rule

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References(17)

References

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