Constructing a sequence of discrete Hessian matrices of an SC
1 function uniformly convergent to the generalized Hessian matrix |
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Authors: | Nezam Mahdavi-Amiri Rohollah Yousefpour |
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Institution: | (1) Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran |
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Abstract: | We construct a uniform approximation for generalized Hessian matrix of an SC
1 function. Using the discrete gradient and the extended second order derivative, we define the discrete Hessian matrix. We
construct a sequence of sets, where each set is composed of discrete Hessian matrices. We first show some new properties of
SC
1 functions. Then, we prove that for SC
1 functions the sequence of the set of discrete Hessian matrices is uniformly convergent to the generalized Hessian matrix.
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Keywords: | Discrete Hessian matrix Generalized Hessian matrix Uniform approximation SC 1 functions Semismoothness |
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