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Minimal approximate Hessians for continuously Gâteaux differentiable functions
Published online by Cambridge University Press: 17 February 2009
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 Gâteaux differentiable function. Finally some necessary and sufficient optimality conditions are presented.
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- Research Article
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- Copyright © Australian Mathematical Society 2004