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An interior point method for a parabolic optimal control problem with regularized pointwise state constraints
Author(s) -
Prüfert U.,
Tröltzsch F.
Publication year - 2007
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.200610337
Subject(s) - pointwise , interior point method , regularization (linguistics) , mathematics , optimal control , pointwise convergence , convergence (economics) , transformation (genetics) , mathematical optimization , path (computing) , state (computer science) , state space , control theory (sociology) , control (management) , computer science , mathematical analysis , algorithm , approx , biochemistry , chemistry , artificial intelligence , economics , gene , programming language , economic growth , operating system , statistics
A primal‐dual interior point method for state‐constrained parabolic optimal control problems is considered. By a Lavrentiev type regularization, the state constraints are transformed to mixed control‐state constraints which, after a simple transformation, can be handled as control constraints. Existence and convergence of the central path are shown. Moreover, the convergence of a short step interior point algorithm is proven in a function space setting. The theoretical properties of the algorithm are confirmed by numerical examples.