Minimal approximate Hessians for continuously Gateaux differentiable functions

• Autores: H. Li, F. Huang
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 45, Nº 3, 2004, págs. 349-360
• Idioma: inglés
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• Resumen

  • 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.