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.
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This research was carried out while the second author was being supported by the National Research Council of Italy at the Numerical Optimization Center of the Hatfield Polytechnic.
Communicated by D. F. Lawden
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Dixon, L.C.W., Gaviano, M. Reflections on nondifferentiable optimization, part 2, convergence. J Optim Theory Appl 32, 259–275 (1980). https://doi.org/10.1007/BF00934553
- Nondifferentiable optimization
- ball gradients