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 languageEnglish (US)
Pages (from-to)290-296
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume253
Issue number1
DOIs
StatePublished - Jan 1 2001

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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

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