The minimization of a maximum‐norm functional subject to an elliptic PDE and state constraints | Zendy

Prüfert U. | Zendy; Schiela A. | Zendy

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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.

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