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High Order Whitney Forms on Simplices and the Question of Potentials Read chapter Read first chapter

2021 | OriginalPaper | Chapter

An Adaptive Penalty Method for Inequality Constrained Minimization Problems

Authors : W. M. Boon, J. M. Nordbotten

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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Abstract

The primal-dual active set method is observed to be the limit of a sequence of penalty formulations. Using this perspective, we propose a penalty method that adaptively becomes the active set method as the residual of the iterate decreases. The adaptive penalty method (APM) therewith combines the main advantages of both methods, namely the ease of implementation of penalty methods and the exact imposition of inequality constraints inherent to the active set method. The scheme can be considered a quasi-Newton method in which the Jacobian is approximated using a penalty parameter. This spatially varying parameter is chosen at each iteration by solving an auxiliary problem.

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previous chapter A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models
next chapter Multipreconditioning with Application to Two-Phase Incompressible Navier–Stokes Flow
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Metadata
Title
An Adaptive Penalty Method for Inequality Constrained Minimization Problems
Authors
W. M. Boon
J. M. Nordbotten
Copyright Year
2021
Book
Numerical Mathematics and Advanced Applications ENUMATH 2019

Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-55874-1_14

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