Abstract
One of the most useful tools developed for use in nonsmooth optimization is the generalized gradient set of Clarke. These gradients have been used on a variety of problems including necessary conditions for optimality, control theory and differential inclusions. Three different techniques can be used to define Clarke’s gradients. They have characterizations in terms of directional derivatives [Clarke (1975), Rockafellar (1980)], the normal cone to the epigraph of a function [Clarke (1975)] and in terms of limits of proximal subgradients [Rockafellar (1981)]. Some of the strongest results involving Clarke’s subgradients have been derived using the proximal subgradient formula [Rockafellar (1982)].
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References
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Treiman, J.S. (1985). A New Approach to Clarke’s Gradients in Infinite Dimensions. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_8
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DOI: https://doi.org/10.1007/978-3-662-12603-5_8
Publisher Name: Springer, Berlin, Heidelberg
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