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The minimization of a maximum‐norm functional subject to an elliptic PDE and state constraints
Author(s) -
Prüfert U.,
Schiela A.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800097
Subject(s) - mathematics , pointwise , norm (philosophy) , differentiable function , optimal control , maximum principle , minification , uniform norm , mathematical optimization , mathematical analysis , political science , law
We study the optimal control of a maximum‐norm objective functional subjected to an elliptic‐type PDE and pointwise state constraints. The problem is transformed into a problem where the non‐differentiable maximum‐norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.