Abstract
In considering the nondifferentiable optimization problem, a new concept is introduced, known as the ball gradient. The ball-gradient magnitude is positive at any local minimum point, independently of whether the minimum point is well behaved, a cusp, or a sheet minimum. The ball-gradient magnitude is negative outside a ball of radius ε around a local minimum point and thus is usable as a terminating criterion on nondifferentiable functions.
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Communicated by D. F. Lawden
The author acknowledges many helpful discussions with Dr. M. Gaviano during the redrafting of this report.
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Dixon, L.C.W. Reflections on nondifferentiable optimization, part 1, ball gradient. J Optim Theory Appl 32, 123–133 (1980). https://doi.org/10.1007/BF00934719
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DOI: https://doi.org/10.1007/BF00934719