Adaptive Smoothing Method, Deterministically Computable Generalized Jacobians, and the Newton Method

H. Xu

Journal of Optimization Theory and Applications, 2001, vol. 109, issue 1, No 12, 215-224

Abstract: Abstract In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an ∈-subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations.

Keywords: Clarke generalized Jacobians; plenary hulls; adaptive smoothing methods; generalized Newton methods (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017526207997

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