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Parametric Method for Global Optimization

Author

Listed:
  • S. De Marchi

    (University of Verona)

  • I. Raykov

    (Ohio University)

Abstract

This paper considers constrained and unconstrained parametric global optimization problems in a real Hilbert space. We assume that the gradient of the cost functional is Lipschitz continuous but not smooth. A suitable choice of parameters implies the linear or superlinear (supergeometric) convergence of the iterative method. From the numerical experiments, we conclude that our algorithm is faster than other existing algorithms for continuous but nonsmooth problems, when applied to unconstrained global optimization problems. However, because we solve 2n + 1 subproblems for a large number n of independent variables, our algorithm is somewhat slower than other algorithms, when applied to constrained global optimization.

Suggested Citation

  • S. De Marchi & I. Raykov, 2006. "Parametric Method for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 411-430, September.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:3:d:10.1007_s10957-006-9118-4
    DOI: 10.1007/s10957-006-9118-4
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    References listed on IDEAS

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    1. Daniel Ralph, 1994. "Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 352-389, May.
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    Cited by:

    1. Efstratios Pistikopoulos & Luis Dominguez & Christos Panos & Konstantinos Kouramas & Altannar Chinchuluun, 2012. "Theoretical and algorithmic advances in multi-parametric programming and control," Computational Management Science, Springer, vol. 9(2), pages 183-203, May.
    2. N. Pavel & I. Raykov, 2008. "Parametric Proximal-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 85-107, October.

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