Result: SIMULTANEOUS SOLUTION OF LINEAR EQUATIONS AND INEQUALITIES IN MAX-ALGEBRA
Title:
SIMULTANEOUS SOLUTION OF LINEAR EQUATIONS AND INEQUALITIES IN MAX-ALGEBRA
Authors:
Source:
Kybernetika. 47(2):241-250
Publisher Information:
Praha: Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic, 2011.
Publication Year:
2011
Physical Description:
print, 12 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Mathematics, Mathématiques, 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, 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, Flots dans les réseaux. Problèmes combinatoires, Flows in networks. Combinatorial problems, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Automatique théorique. Systèmes, Control theory. Systems, Analyse des systèmes de commande, Control system analysis, Algèbre linéaire, Linear algebra, Algebra lineal, Algèbre max, Max algebra, Algebra max, Condition nécessaire suffisante, Necessary and sufficient condition, Condición necesaria suficiente, Contrainte, Constraint, Coacción, Equation linéaire, Linear equation, Ecuación lineal, Inégalité, Inequality, Desigualdad, Modélisation, Modeling, Modelización, Méthode polynomiale, Polynomial method, Método polinomial, Optimisation combinatoire, Combinatorial optimization, Optimización combinatoria, Programmation linéaire, Linear programming, Programación lineal, Programmation non convexe, Non convex programming, Programación no convexa, Résolubilité, Solvability, Resolubilidad, Temps polynomial, Polynomial time, Tiempo polinomial, 15A06, 15A39, 90C26, 90C27, linear equations and inequalities, max-algebra, max-linear programming
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematical Sciences, Kano University of Science and Technology, Wudil, P.M.B 3244, Kano, Nigeria
ISSN:
0023-5954
Rights:
Copyright 2015 INIST-CNRS
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
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:
Computer science; theoretical automation; systems
Mathematics
Operational research. Management
Mathematics
Operational research. Management
Accession Number:
edscal.24321705
Database:
PASCAL Archive
Further Information
Let a⊕b = max(a,b) and a⊗b = a + b for a, b ∈ ℝ. Max-algebra is an analogue of linear algebra developed on the pair of operations (⊕, ⊗) extended to matrices and vectors. The system of equations A ⊗ x = b and inequalities C ⊗ x ≤ d have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities.