Inexact primal-dual interior point iteration for linear programs in function spaces |
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| Authors: | S. Ito C. T. Kelley E. W. Sachs |
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| Affiliation: | (1) Department of Prediction and Control, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, 106 Minato-ku, Tokyo, Japan;(2) Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Box 8205, 27695-8205 Raleigh, N.C.;(3) FB IV-Mathematik, Universität Trier, D-54286 Trier, Federal Republic of Germany |
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| Abstract: | Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.The research of this author was supported by an Overseas Research Scholarship of the Ministry of Education, Science and Culture of Japan.The research of this author was supported by National Science Foundation grants #DMS-9024622 and #DMS-9321938, North Atlantic Treaty Organization grant #CRG 920067, and an allocation of computing resources from the North Carolina Supercomputing Program.The research of this author was supported by North Atlantic Treaty Organization grant #CRG 920067. |
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| Keywords: | state constrained optimal control problem primal-dual interior point algorithm linear programming inexact Newton method |
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