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

^*Corresponding author for this work

Institute of Information Management

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	290-296
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	253
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.2000.7115
State	Published - 1 Jan 2001

Keywords

Convex function; Fréchet differentiable; quadratic programming

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10.1006/jmaa.2000.7115

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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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AU - Matache, Valentin

AU - Yu, Po Lung

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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.

KW - Convex function; Fréchet differentiable; quadratic programming

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

Abstract

Keywords

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