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Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient

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Minimization Methods for Non-Differentiable Functions

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 3))

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When solving many mathematical programming problems one has to consider a broader class of functions than that of continuously differentiable functions. In such cases We, as a rule, deal with continuous and almost everywhere differentiable functions, whose gradient is discontinuous on a set of null measure. Although in principle functions may arise with even greater pathology (for example, functions that are nowhere differentiable on a set of positive measure), such functions are not encountered in practice; moreover, construction of any nontrivial algorithm for minimizing such functions does not appear possible.

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© 1985 Springer-Verlag Berlin, Heidelberg

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Shor, N.Z. (1985). Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient. In: Minimization Methods for Non-Differentiable Functions. Springer Series in Computational Mathematics, vol 3. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82120-2

  • Online ISBN: 978-3-642-82118-9

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