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Fractional Programming

Theory, Methods and Applications

  • Book
  • © 1997

Overview

Authors:
  1. I. M. Stancu-Minasian

    1. Centre for Mathematical Statistics, The Romanian Academy, Bucharest, Romania

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Part of the book series: Mathematics and Its Applications (MAIA, volume 409)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • I. M. Stancu-Minasian
    Pages 1-5

  3. Fractional Programming Applications

    • I. M. Stancu-Minasian
    Pages 6-33

  4. Convex, Quasiconvex, Pseudoconvex, Logarithmic Convex, αm-Convex, and Invex Functions

    • I. M. Stancu-Minasian
    Pages 34-61

  5. Methods For Solving Linear Fractional Programming Problems

    • I. M. Stancu-Minasian
    Pages 62-132

  6. Nonlinear Fractional Programming

    • I. M. Stancu-Minasian
    Pages 133-162

  7. Duality in Fractional Programming

    • I. M. Stancu-Minasian
    Pages 163-185

  8. Fractional Programming with Multiple Objective Functions

    • I. M. Stancu-Minasian
    Pages 186-206

  9. Fractional Programming in The Complex Space

    • I. M. Stancu-Minasian
    Pages 207-237

  10. Special Linear Fractional Programming Problems

    • I. M. Stancu-Minasian
    Pages 238-307

  11. Integer and Mixed Integer Linear Fractional Programming

    • I. M. Stancu-Minasian
    Pages 308-335

  12. Fractional Transportation Problem

    • I. M. Stancu-Minasian
    Pages 336-364

  13. Back Matter

    Pages 365-418
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Keywords

About this book

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.

Authors and Affiliations

  • Centre for Mathematical Statistics, The Romanian Academy, Bucharest, Romania

    I. M. Stancu-Minasian

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