Trees and hills: methodology for maximizing functions of systems of linear relations
type: Item
instance of: scholarly article
title: Trees and hills: methodology for maximizing functions of systems of linear relations
zbMATH Open document ID: 0642.90066
author: Rick Greer
published in: Annals of Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: This monograph introduces the problem of extremizing functions of systems of linear relations subject to constraints. There are many problems which fall into this category, e.g., the problem of finding solutions to consistent systems of linear inequalities, the linear programming problem, and the problem of finding solutions to systems of linear equations. The author suggests the so-called tree algorithm for solving problems of this class. After having introduced the reader to that part of the theory of polyhedral convex cones which is needed to understand the nature of the tree algorithm (Chapter 2), the author describes a special and then a general version of the tree algorithm and discusses its computational complexity (Chapters 3-6). Chapter 7 is devoted to the comparison of the tree algorithm with other procedures for extremizing functions of systems of linear relations. Various applications of the tree algorithm are surveyed in Chapter 8. Chapter 9 discusses examples of the behaviour of the tree algorithm in practice. The results are summarized in the concluding Chapter 10.
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 90-02
zbMATH DE Number: 4047433
zbMATH Keywords: functions of systems of linear relations
zbMATH Keywords: tree algorithm
zbMATH Keywords: polyhedral convex cones
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4047433