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Systems of linear inequalities

Author: A S Solodovnikov
Publisher: Chicago : University of Chicago Press, 1980.
Series: Popular lectures in mathematics.; Survey of recent East European mathematical literature.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This volume describes the relationship between systems of linear inequalities and the geometry of convex polygons, examines solution sets for systems of linear inequalities in two and three unknowns (extension of the processes introduced to systems in any number of unknowns is quite simple), and examines questions of the consistency or inconsistency of such systems. Finally, it discusses the field of linear  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A S Solodovnikov
ISBN: 0226767868 9780226767864
OCLC Number: 5126287
Notes: Translation of Sistemy lineĭnykh neravenstv.
Description: viii, 81 pages : illustrations ; 23 cm.
Contents: Several facts from analytic geometry --
Geometric interpretation of a system of linear inequalities in two and three unknowns --
The convex hull of a point set --
Convex polyhedral cones --
The solution domain of a system of inequalities in two unknowns --
The solution domain of a system in three unknowns --
Systems of linear inequalities in a arbitrary number of unknowns --
Inconsistent systems --
Dual convex polyhedral cones --
The duality theorem of linear programming.
Series Title: Popular lectures in mathematics.; Survey of recent East European mathematical literature.
Other Titles: Sistemy lineĭnykh neravenstv.
Responsibility: A.S. Solodovnikov ; translated and adapted from the Russian ed. by Lawrence M. Glasser and Thomas P. Branson.
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Abstract:

This volume describes the relationship between systems of linear inequalities and the geometry of convex polygons, examines solution sets for systems of linear inequalities in two and three unknowns (extension of the processes introduced to systems in any number of unknowns is quite simple), and examines questions of the consistency or inconsistency of such systems. Finally, it discusses the field of linear programming, one of the principal applications of the theory of systems of linear inequalities. A proof of the duality theorem of linear programming is presented in the last section. --Back cover.

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