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Constructing a sequence of discrete Hessian matrices of an SC1 function uniformly convergent to the generalized Hessian matrix

Mahdavi Amiri, N ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s10107-008-0238-5
  3. Abstract:
  4. We construct a uniform approximation for generalized Hessian matrix of an SC1 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 SC1 functions. Then, we prove that for SC1 functions the sequence of the set of discrete Hessian matrices is uniformly convergent to the generalized Hessian matrix
  5. Keywords:
  6. Discrete Hessian matrix ; Generalized Hessian matrix ; SC1 functions ; Mathematical programming ; Discrete gradient ; Hessian matrices ; Second order derivatives ; Semismoothness ; Uniform approximation ; Uniformly convergent ; Software engineering
  7. Source: Mathematical Programming ; Volume 121, Issue 2 , 2010 , Pages 387-414 ; 00255610 (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs10107-008-0238-5