Synopses & Reviews
This volume aims to present the state-of-the-art in the theory and practice of fractional programming in an orderly form. Possible fields of application for fractional programming methods are given first. Next, among others, the convex, quasi-convex, pseudo-convex, and log-convex functions are described. Methods for solving linear fractional programming problems, as well as non-linear problems are introduced and examined. Duality, multiple-objective, mathematical programming in complex space, integer and mixed integer subjects as applied to fractional programming are treated separately. Special problems and fractional transportation problems are also treated. Audience: This book will be of interest to mathematicians, engineers, economists whose work involves the application of optimization theory.
Synopsis
Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances, especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume, cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decades.
Table of Contents
Introduction. 1. Fractional Programming Applications. 2. Convex, Quasiconvex, Pseudoconvex, Logarithmic Convex, alpham-Convex, and Invex Functions. 3. Methods for Solving Linear Fractional Programming Problems. 4. Nonlinear Fractional Programming. 5. Duality in Fractional Programming. 6. Fractional Programming with Multiple Objective Functions. 7. Fractional Programming in the Complex Space. 8. Special Linear Fractional Programming Problems. 9. Integer and Mixed Integer Linear Fractional Programming. 10. Fractional Transportation Problem. Bibliography. Subject Index. Author Index.