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An interior penalty approach to a large-scale discretized obstacle problem with nonlinear constraints

Authors :
Jian-Xun Zhao
Song Wang
Source :
Numerical Algorithms. 85:571-589
Publication Year :
2020
Publisher :
Springer Science and Business Media LLC, 2020.

Abstract

We propose an interior penalty method to solve a nonlinear obstacle problem arising from the discretization of an infinite-dimensional optimization problem. An interior penalty equation is proposed to approximate the mixed nonlinear complementarity problem representing the Karush-Kuhn-Tucker conditions of the obstacle problem. We prove that the penalty equation is uniquely solvable and present a convergence analysis for the solution of the penalty equation when the problem is strictly convex. We also propose a Newton’s algorithm for solving the penalty equation. Numerical experiments are performed to demonstrate the convergence and usefulness of the method when it is used for the two non-trivial test problems.

Details

ISSN :
15729265 and 10171398
Volume :
85
Database :
OpenAIRE
Journal :
Numerical Algorithms
Accession number :
edsair.doi...........8d0141254a6065b7a3f50ff2a48daa82
Full Text :
https://doi.org/10.1007/s11075-019-00827-2