A Necessary and Sufficient Condition for Minimizing a Convex Fréchet Differentiable Function on a Certain Hyperplane

Han-Lin Li; Yi Hsin Liu; Valentin Matache; Po Lung Yu

doi:10.1006/jmaa.2000.7115

A Necessary and Sufficient Condition for Minimizing a Convex Fréchet Differentiable Function on a Certain Hyperplane

Han-Lin Li^*, Yi Hsin Liu, Valentin Matache, Po Lung Yu

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摘要

A convex Fréchet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic.

原文	English
頁（從 - 到）	290-296
頁數	7
期刊	Journal of Mathematical Analysis and Applications
卷	253
發行號	1
DOIs	https://doi.org/10.1006/jmaa.2000.7115
出版狀態	Published - 1 1月 2001

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abstract = "A convex Fr{\'e}chet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic.",

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AB - A convex Fréchet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic.

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A Necessary and Sufficient Condition for Minimizing a Convex Fréchet Differentiable Function on a Certain Hyperplane

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