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Directional Derivatives of Difference Functions of Nonsmooth Max-functions

Directional Derivatives of Difference Functions of Nonsmooth Max-functions
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摘要 In this paper, we give an upper estimate for the Clarke-Rockafellar directional derivatives of a function of the form f - g, where f, g are max-functions defined by locally Lipschitz but not necessarily differentiable functions on a closed convex set in a Euclidean space. As an application, we give a sufficient condition for f - g to have an error bound. In this paper, we give an upper estimate for the Clarke-Rockafellar directional derivatives of a function of the form f - g, where f, g are max-functions defined by locally Lipschitz but not necessarily differentiable functions on a closed convex set in a Euclidean space. As an application, we give a sufficient condition for f - g to have an error bound.
作者 Lu-lin Tan
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第3期495-502,共8页 应用数学学报(英文版)
基金 Supported by the National Natural Science Foundation of China (No. 10801137)
关键词 Clarke-rockafellar directional derivatives generalized directional derivatives rademacher theorem dini-directional derivatives max-functions error bound Clarke-rockafellar directional derivatives, generalized directional derivatives, rademacher theorem,dini-directional derivatives, max-functions, error bound
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参考文献8

  • 1Clarke, F.H. Optimization and nonsmooth analysis. John Wiley, New York, 1983.
  • 2Fadell, A.G. A generalization of Rademacher's theorem on complete differential. Colloquium Mathematicum, 27:126-131 (1973).
  • 3Ng, K.F., Zheng, X.Y. Error bound for lower semicontinuous functions in normed space. SIAM Journal on Optimization, 12:1-17 (2001).
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  • 7Ng, K.F., Tan, L.L. Error bounds of regularized gap functions for nonsmooth variational inequality prob- lems. Mathematical Programming, 110:405-429 (2007).
  • 8Zalinescu, C. Convex analysis in general vector spaces. World Scientific, Singapore, 2002.

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