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State‐Constrained Optimization of PDEs via Infinite Penalization Methods
Author(s) -
Barnard Richard,
Frank Martin,
Herty Michael
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210334
Subject(s) - partial differential equation , mathematics , elliptic partial differential equation , state (computer science) , mathematical optimization , optimization problem , mathematical analysis , algorithm
We consider optimization problems constrained by partial differential equations (PDEs) with additional constraints placed on the solution of the PDEs. Specifically, we consider problems involving constraints on the average value of the state in subdomains. We develop a general framework using infinite‐valued penalization functions and Clarke generalized gradients to obtain optimality conditions. A numerical example involving a linear elliptic PDE is presented. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)