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Algorithms for Unconstrained Optimization Problems via Control Theory

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  • B. S. Goh

    (University of Western Australia)

Abstract

Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem.

Suggested Citation

  • B. S. Goh, 1997. "Algorithms for Unconstrained Optimization Problems via Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 581-604, March.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:3:d:10.1023_a:1022607507153
    DOI: 10.1023/A:1022607507153
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    Citations

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    Cited by:

    1. Iasson Karafyllis, 2014. "Feedback Stabilization Methods for the Solution of Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 783-806, June.
    2. B. S. Goh, 2010. "Convergence of Algorithms in Optimization and Solutions of Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 43-55, January.
    3. B. S. Goh, 2009. "Greatest Descent Algorithms in Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 275-289, August.
    4. Isaac M. Ross, 2023. "Derivation of Coordinate Descent Algorithms from Optimal Control Theory," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    5. B. S. Goh, 2011. "Approximate Greatest Descent Methods for Optimization with Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 505-527, March.

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