Treffer: On a commutative class of search directions for linear programming over symmetric cones

Title:
On a commutative class of search directions for linear programming over symmetric cones
Authors:
MURAMATSU, M
Source:
Journal of optimization theory and applications. 112(3):595-625
Publisher Information:
New York, NY: Springer, 2002.
Publication Year:
2002
Physical Description:
print, 17 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, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, 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, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Programmation mathématique, Mathematical programming, Algèbre, Algebra, Complexité, Complexity, Complejidad, Corps symétrique, Symmetric body, Cuerpo simétrico, Cône, Cone, Cono, Méthode point intérieur, Interior point method, Método punto interior, Méthode primale duale, Primal dual method, Método primal dual, Méthode à pas, Step method, Método a paso, Optimisation, Optimization, Optimización, Polynôme, Polynomial, Polinomio, Programmation convexe, Convex programming, Programación convexa, Programmation linéaire, Linear programming, Programación lineal, Programmation semi définie, Semi definite programming, Programacíon semi definida
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Science, The University of Electro-Communications, Chofu-Shi, Tokyo, Japan
ISSN:
0022-3239
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=14263001
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
Notes:
Mathematics

Operational research. Management
Accession Number:
edscal.14263001
Database:
PASCAL Archive

Weitere Informationen

The commutative class of search directions for semidefinite programming was first proposed by Monteiro and Zhang (Ref. 1). In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Complexity results are established for short-step, semilong-step, and long-step algorithms. Then, we propose a subclass of the commutative class for which we can prove polynomial complexities of the interior-point method using semilong steps and long steps. This subclass still contains the Nesterov-Todd direction and the Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro direction. An explicit formula to calculate any member of the class is also given.