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Let $\vec g(\vec x)\in\mathbb R^N$ be the gradient of a convex function $L: \mathbb R^N\mapsto \mathbb R$ and $\vec h(\vec x)$ such that $$ \vec h(\vec x)^T\vec g(\vec x) \geq 0\quad\quad \forall \vec x\in\mathbb R^N. $$ Than, under weak conditions, a gradient ascent in direction $\vec h$ will lead to the maximum of $L$.

Question: What is the correct mathematical expression or "buzzword" for $\vec h$? "Quasigradient"? "Approximate gradient"? The concept is so trivial yet I can't figure out the appropriate name.

Thanks!

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"an ascending direction"? –  Hagen von Eitzen May 2 '13 at 22:13
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