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.
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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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Ito, S., Kelley, C.T. & Sachs, E.W. Inexact primal-dual interior point iteration for linear programs in function spaces. Comput Optim Applic 4, 189–201 (1995). https://doi.org/10.1007/BF01300870
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DOI: https://doi.org/10.1007/BF01300870
Keywords
- state constrained optimal control problem
- primal-dual interior point algorithm
- linear programming
- inexact Newton method