Linear-Fractional Programming Theory, Methods, Applications and Software: 84 (Applied Optimization, 84) - Hardcover

Bajalinov, E.B.

Hardcover

ISBN 10: 1402076266 ISBN 13: 9781402076268

Publisher: Springer, 2003

Synopsis

This is a book on Linear-Fractional Programming (here and in what follows we will refer to it as "LFP"). The field of LFP, largely developed by Hungarian mathematician B. Martos and his associates in the 1960's, is concerned with problems of op­ timization. LFP problems deal with determining the best possible allo­ cation of available resources to meet certain specifications. In particular, they may deal with situations where a number of resources, such as people, materials, machines, and land, are available and are to be combined to yield several products. In linear-fractional programming, the goal is to determine a per­ missible allocation of resources that will maximize or minimize some specific showing, such as profit gained per unit of cost, or cost of unit of product produced, etc. Strictly speaking, linear-fractional programming is a special case of the broader field of Mathematical Programming. LFP deals with that class of mathematical programming problems in which the relations among the variables are linear: the con­ straint relations (i.e. the restrictions) must be in linear form and the function to be optimized (i.e. the objective function) must be a ratio of two linear functions.

About this title

Review

From the reviews:

"Although several books on general (nonlinear) fractional programming are available, this is the first monograph entirely devoted to linear-fractional problems. As the title indicates, it deals with both the theoretical and the algorithmic aspects of the subject, including the description of a program package for Windows." (Juan-Enrique Martínez-Legaz, Zentralblatt MATH, Vol. 1067 (18), 2005)

Synopsis

Unlike other fractional programming related titles, this book offers a "direct" approach to LFP and to duality in LFP, which is new in many aspects. First, the original LFP problem is considered as it is, without reducing it to an LP problem. Moreover, LFP is considered to be a generalization of LP and so most of the results are formulated in such a way that appropriate results of LP may be obtained as a special case of LFP. On the other hand, this approach makes it possible to compare dual variables in LP and LFP and to describe the relationship between them. In this respect, important (and new) application possibilities of duality appear in different parts of the book. The book provides readers with the basic knowledge necessary to build LFP models, to solve LFP problems and to utilize the optimal solution obtained. Moreover, the book contains detailed information on WinGULF, a software package developed by the author especially for linear-fractional programming. The package is designed to solve LFP problems with continuous as well as integer variables. The special "Student Edition" version of the package is free of charge and may be downloaded from the author's web page.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 1402076266
• ISBN 13: 9781402076268
• Binding: Hardcover
• Number of pages: 453