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A New Steepest Descent Differential Inclusion-Based Method for Solving General Nonsmooth Convex Optimization Problems

Author

Listed:
  • Alireza Hosseini

    (Tarbiat Modares University)

  • S. M. Hosseini

    (Tarbiat Modares University)

Abstract

In this paper, we investigate a steepest descent neural network for solving general nonsmooth convex optimization problems. The convergence to optimal solution set is analytically proved. We apply the method to some numerical tests which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.

Suggested Citation

  • Alireza Hosseini & S. M. Hosseini, 2013. "A New Steepest Descent Differential Inclusion-Based Method for Solving General Nonsmooth Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 698-720, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-012-0258-4
    DOI: 10.1007/s10957-012-0258-4
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    References listed on IDEAS

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    1. X. Zhao & P.B. Luh, 2002. "New Bundle Methods for Solving Lagrangian Relaxation Dual Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 373-397, May.
    2. M. V. Solodov, 2003. "On Approximations with Finite Precision in Bundle Methods for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 151-165, October.
    3. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
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