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

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 p...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 253; no. 1; pp. 290 - 296
Main Authors Li, Han-Lin, Liu, Yi-Hsin, Matache, Valentin, Yu, Po-Lung
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.01.2001
Elsevier
Subjects
Algebra
Applied sciences
Calculus of variations and optimal control
convex function
Exact sciences and technology
Fréchet differentiable
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematical programming
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Operational research and scientific management
Operational research. Management science
quadratic programming
Sciences and techniques of general use
convex function
quadratic programming
Fréchet differentiable
Lagrange multiplier
Differntiable function
Fréchet differentiability
Necessary and sufficient condition
Minimization
Convex function
Quadratic programming
Differentiable manifold
Mathematical programming
Equation system
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2000.7115