ANZIAM J.
45 (2004), 349-359
|
Minimal approximate Hessians for continuously Gateaux differentiable functions
|
Hongxu Li
Department of Mathematics
Sichuan University
Chengdu
Sichuan 610064
P. R. China
Hoxuli@sohu.com
|
|
|
Falun Huang
Department of Mathematics
Sichuan University
Chengdu
Sichuan 610064
P. R. China
|
|
|
Abstract
|
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
Gateaux differentiable function. Finally some
necessary and sufficient optimality conditions
are presented.
|
Download the article in PDF format (size 97 Kb)
|
|
|
|