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Pseudoconvex function : ウィキペディア英語版 | Pseudoconvex function
In convex analysis and the calculus of variations, branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex. Informally, a differentiable function is pseudoconvex if it is increasing in any direction where it has a positive directional derivative. ==Formal definition== Formally, a real-valued differentiable function ''ƒ'' defined on a (nonempty) convex open set ''X'' in the finite-dimensional Euclidean space R''n'' is said to be pseudoconvex if, for all such that , we have . Here ∇''ƒ'' is the gradient of ''ƒ'', defined by :
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Pseudoconvex function」の詳細全文を読む
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