# 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

Research output: Contribution to journalArticle

### 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 (US) 290-296 7 Journal of Mathematical Analysis and Applications 253 1 https://doi.org/10.1006/jmaa.2000.7115 Published - Jan 1 2001

### Fingerprint

Hyperplane
Differentiable
Necessary Conditions
Set of vectors
Sufficient Conditions
Lagrange multipliers
Linear Program
Convex function
Finite Set

### Keywords

• Convex function; Fréchet differentiable; quadratic programming

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics

### Cite this

A Necessary and Sufficient Condition for Minimizing a Convex Fréchet Differentiable Function on a Certain Hyperplane. / Li, Han Lin; Liu, Yi Hsin; Matache, Valentin; Yu, Po Lung.

In: Journal of Mathematical Analysis and Applications, Vol. 253, No. 1, 01.01.2001, p. 290-296.

Research output: Contribution to journalArticle

title = "A Necessary and Sufficient Condition for Minimizing a Convex Fr{\'e}chet Differentiable Function on a Certain Hyperplane",
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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author = "Li, {Han Lin} and Liu, {Yi Hsin} and Valentin Matache and Yu, {Po Lung}",
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journal = "Journal of Mathematical Analysis and Applications",
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AU - Liu, Yi Hsin

AU - Matache, Valentin

AU - Yu, Po Lung

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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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KW - Convex function; Fréchet differentiable; quadratic programming

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