Volume no :4, Issue no: 2, March 2010

GENERALIZED MATRICES FOR LIPSCHITZ FUNCTIONS

Author's: I. M. Proudnikov
Pages: [227] - [244]
Received Date: April 1, 2009; Revised June 7, 2009
Submitted by: Zeyad Abdel Aziz Mah’d Al Zhour.

Abstract

It is proved that matrices of the second mixed derivatives of the support function for an introduced set-valued mapping for Lipschitz function exist almost everywhere in Matrices are similar to matrices of second derivatives for smooth functions. The Clarke subdifferential of the set-valued mapping generalized and their continuous extension generalized matrices for were defined. Under some assumption, a continuous extension of the Clarke, subdifferential and the form of when is twice continuous differentiable were found. An optimization method is proposed for using these matrices in nonsmooth optimization.

Keywords

Lipschitz functions, Lipschitz set-valued mappings, support function, generalized matrices for Lipschitz functions, Clarke subdifferential for set-valued mappings, Newton’s optimization process.