Result: Mathematical properties of optimization problems defined by positively homogeneous functions
Title:
Mathematical properties of optimization problems defined by positively homogeneous functions
Authors:
Source:
Journal of optimization theory and applications. 112(1):31-52
Publisher Information:
New York, NY: Springer, 2002.
Publication Year:
2002
Physical Description:
print, 15 ref
Original Material:
CRAN
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Analyse non convexe, Non convex analysis, Análisis no convexo, Minimisation, Minimization, Minimización, Méthode minimax, Minimax method, Método minimax, Optimisation, Optimization, Optimización, Optimum global, Global optimum, Optimo global, Programmation convexe, Convex programming, Programación convexa, Programmation linéaire, Linear programming, Programación lineal, Programmation non convexe, Non convex programming, Programación no convexa, Programmation non linéaire, Non linear programming, Programación no lineal
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
LAAS-CNRS, Toulouse, France
Département de Mathématiques, Université Paul Sabatier, Toulouse, France
Département de Mathématiques, Université Paul Sabatier, Toulouse, France
ISSN:
0022-3239
Rights:
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.14246909
Database:
PASCAL Archive
Further Information
We consider the nonlinear programming problem (J)→{min f(x)|gl(x)≤bi, i = 1,…,m}, with f positively p-homogeneous and gi positively q-homogeneous functions. We show that (J) admits a simple min-max formulation (D) with the inner max-problem being a trivial linear program with a single constraint. This provides a new formulation of the linear programming problem and the linear-quadratic one as well. In particular, under some conditions, a global (nonconvex) optimization problem with quadratic data is shown to be equivalent to a convex minimization problem.