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In vector calculus, an invex function is a differentiable function ''ƒ'' from R''n'' to R for which there exists a vector valued function ''g'' such that : for all ''x'' and ''u''. Invex functions were introduced by Hanson 〔M.A. Hanson, On sufficiency of the Kuhn–Tucker conditions, J. Math. Anal. Appl. 80, pp. 545–550 (1981)〕 as a generalization of convex functions. Ben-Israel and Mond 〔Ben-Israel, A. and Mond, B., What is invexity?, The ANZIAM Journal 28, pp. 1–9 (1986)〕 provided a simple proof that a function is invex if and only if every stationary point is a global minimum. Hanson also showed that if the objective and the constraints of an optimization problem are invex with respect to the same function ''g''(''x'', ''u''), then the Karush–Kuhn–Tucker conditions are sufficient for a global minimum. A slight generalization of invex functions called Type 1 invex functions are the most general class of functions for which the Karush–Kuhn–Tucker conditions are necessary and sufficient for a global minimum.〔M.A. Hanson, Invexity and the Kuhn-Tucker Theorem, J. Math. Anal. Appl. vol. 236, pp. 594–604 (1999)〕 ==See also== * Convex function * Pseudoconvex function * Quasiconvex function 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「Invex function」の詳細全文を読む スポンサード リンク
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