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Minimal approximate Hessians for continuously Gâteaux differentiable functions

Published online by Cambridge University Press:  17 February 2009

Hongxu Li  and
Falun Huang
Hongxu Li
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China; e-mail: Hoxuli@sohu.com.
Falun Huang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China; e-mail: Hoxuli@sohu.com.
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Abstract

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In this paper, we investigate minimal (weak) approximate Hessians, and completely answer the open questions raised by V. Jeyakumar and X. Q. Yang. As applications, we first give a generalised Taylor's expansion in terms of a minimal weak approximate Hessian. Then we characterise the convexity of a continuously Gâteaux differentiable function. Finally some necessary and sufficient optimality conditions are presented.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 3 , January 2004 , pp. 349 - 359
Copyright
Copyright © Australian Mathematical Society 2004

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