Fractional Programming

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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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.

• Optimization Theory
• duality
• linear optimization
• mathematical programming
• optimization

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

  I. M. Stancu-Minasian

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