Euler Discretization and Inexact Restoration for Optimal Control |
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| Authors: | C Y Kaya J M Martínez |
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| Institution: | 1.School of Mathematics and Statistics,University of South Australia,Mawson Lakes,Australia;2.Departamento de Sistemas e Computa??o,Universidade Federal do Rio de Janeiro,Rio de Janeiro,Brazil;3.Department of Applied Mathematics, IMECC-UNICAMP,University of Campinas,Campinas,Brazil |
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| Abstract: | A computational technique for unconstrained optimal control problems is presented. First, an Euler discretization is carried
out to obtain a finite-dimensional approximation of the continuous-time (infinite-dimensional) problem. Then, an inexact restoration
(IR) method due to Birgin and Martínez is applied to the discretized problem to find an approximate solution. Convergence
of the technique to a solution of the continuous-time problem is facilitated by the convergence of the IR method and the convergence
of the discrete (approximate) solution as finer subdivisions are taken. The technique is numerically demonstrated by means
of a problem involving the van der Pol system; comprehensive comparisons are made with the Newton and projected Newton methods. |
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| Keywords: | Optimal control Inexact restoration Euler discretization Projected Newton method Lagrange multiplier update |
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