On the interplay between interior point approximation and parametric sensitivities in optimal control |
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Authors: | Roland Griesse Martin Weiser |
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Institution: | a Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria b Zuse Institute Berlin, Takustrasse 7, D-14195 Berlin, Germany |
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Abstract: | Infinite-dimensional parameter-dependent optimization problems of the form ‘minJ(u;p) subject to g(u)?0’ are studied, where u is sought in an L∞ function space, J is a quadratic objective functional, and g represents pointwise linear constraints. This setting covers in particular control constrained optimal control problems. Sensitivities with respect to the parameter p of both, optimal solutions of the original problem, and of its approximation by the classical primal-dual interior point approach are considered. The convergence of the latter to the former is shown as the homotopy parameter μ goes to zero, and error bounds in various Lq norms are derived. Several numerical examples illustrate the results. |
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Keywords: | Interior point methods Parametric sensitivity Optimal control |
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