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Journal of Optimization Theory and Applications

, Volume 32, Issue 3, pp 259–275 | Cite as

Reflections on nondifferentiable optimization, part 2, convergence

  • L. C. W. Dixon
  • M. Gaviano
Contributed Papers

Abstract

This paper is concerned with the minimization of nondifferentiable functions. Three main results are obtained: (i) convergence of the ball-gradient algorithm, introduced by Dixon, for convex functions; (ii) convergence of the generalized gradient algorithm, as implemented by Shor and Ermol'ev, to a stationary point; and (iii) convergence of an algorithm introduced by Goldstein to a local minimum.

Key Words

Nondifferentiable optimization subgradients ball gradients 

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References

  1. 1.
    Shor, N. Z.,Generalized Gradient Methods of Minimization of Nonsmoothed Functions and Their Use in Problems of Mathematical Programming (in Russian), Mathematical Methods, Vol. 12, pp. 337–356, 1976.Google Scholar
  2. 2.
    Wolfe, P.,A Method of Conjugate Subgradients for Minimizing Nondifferentiable Functions, Nondifferentiable Optimization, Edited by M. L. Balinski and P. Wolfe, North-Holland Publishing Company, Amsterdam, Holland, 1975.Google Scholar
  3. 3.
    Ermol'ev, J. M.,Methods of Solving Nonlinear Extremal Problems, Kibernetika, Vol. 4, pp. 1–4, 1966.Google Scholar
  4. 4.
    Goldstein, A. A.,Optimization of Lipschitz Continuous Functions, Mathematical Programming, Vol. 13, pp. 14–22, 1977.Google Scholar
  5. 5.
    Dixon, L. C. W.,Reflections on Nondifferentiable Optimization, Part 1, Ball Gradient, Journal of Optimization Theory and Applications, Vol. 32, No. 2, 1980.Google Scholar
  6. 6.
    Polyak, B. T.,A General Method of Solving Extremal Problems, Doklady Akademii Nauk, SSSR, Vol. 174, pp. 593–597, 1967.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • L. C. W. Dixon
    • 1
  • M. Gaviano
    • 2
  1. 1.Numerical Optimization CenterHatfield PolytechnicHatfieldEngland
  2. 2.Istituto MatematicoUniversita' di CagliariCagliariItaly

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