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Euler Discretization and Inexact Restoration for Optimal Control

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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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Authors and Affiliations

  1. School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A., 5095, Australia

    C. Y. Kaya

  2. Departamento de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    C. Y. Kaya

  3. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, Campinas, SP, Brazil

    J. M. Martínez

Authors
  1. C. Y. Kaya
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  2. J. M. Martínez
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Correspondence to C. Y. Kaya.

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Communicated by T.L. Vincent.

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Kaya, C.Y., Martínez, J.M. Euler Discretization and Inexact Restoration for Optimal Control. J Optim Theory Appl 134, 191–206 (2007). https://doi.org/10.1007/s10957-007-9217-x

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