A power penalty approach to a discretized obstacle problem with nonlinear constraints

A novel power penalty method is proposed to solve a nonlinear obstacle problem with nonlinear constraints arising from the discretization of an infinite-dimensional optimization problem. This approach is based on the formulation of a penalty equation approximating the mixed nonlinear complementarity...

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Bibliographic Details
Main Authors: Zhao, J., Wang, Song
Format: Journal Article
Published: Springer Verlag 2019
Online Access:http://hdl.handle.net/20.500.11937/71030
Description
Summary:A novel power penalty method is proposed to solve a nonlinear obstacle problem with nonlinear constraints arising from the discretization of an infinite-dimensional optimization problem. This approach is based on the formulation of a penalty equation approximating the mixed nonlinear complementarity problem arising from the Karush–Kuhn–Tucker conditions of the optimization problem. We show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the penalty equation. Numerical experiments are performed to confirm the theoretical convergence rate established.