Generalized Fractional Programming

Gaston Mandata N’Guerekata
Morgan State University Baltimore, MD, USA

Ram U. Verma
President of International Publications USA

Series: Mathematics Research Developments
BISAC: MAT027000

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This monograph is aimed at presenting smooth and unified generalized fractional programming (or a program with a finite number of constraints). Under the current interdisciplinary computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of its multi-facet applications and empowerment for real world problems that can be handled by transforming them into generalized fractional programming problems. Problems of this type have been applied for the modeling and analysis of a wide range of theoretical as well as concrete, real world, practical problems. More specifically, generalized fractional programming concepts and techniques have found relevance and worldwide applications in approximation theory, statistics, game theory, engineering design (earthquake-resistant design of structures, design of control systems, digital filters, electronic circuits, etc.), boundary value problems, defect minimization for operator equations, geometry, random graphs, graphs related to Newton flows, wavelet analysis, reliability testing, environmental protection planning, decision making under uncertainty, geometric programming, disjunctive programming, optimal control problems, robotics, and continuum mechanics, among others. It is highly probable that among all industries, especially for the automobile industry, robots are about to revolutionize the assembly plants forever. That would change the face of other industries toward rapid technical innovation as well.

The main focus of this monograph is to empower graduate students, faculty and other research enthusiasts for more accelerated research advances with significant applications in the interdisciplinary sense without borders. The generalized fractional programming problems have a wide range of real-world problems, which can be transformed in some sort of a generalized fractional programming problem.

Consider fractional programs that arise from management decision science; by analyzing system efficiency in an economical sense, it is equivalent to maximizing system efficiency leading to fractional programs with occurring objectives:
Maximizing productivity
Maximizing return on investment
Maximizing return/ risk
Minimizing cost/time
Minimizing output/input

The authors envision that this monograph will uniquely present the interdisciplinary research for the global scientific community (including graduate students, faculty, and general readers). Furthermore, some of the new concepts can be applied to duality theorems based on the use of a new class of multi-time, multi-objective, variational problems as well.

Preface

Introduction

Chapter 1. Higher Order Parametric Optimality Conditions (pp. 29-68)

Chapter 2. Hybrid (ö, ç, ù, î, ñ, è, m)-Sonvexities and Parametric Optimality Conditions (pp. 69-92)

Chapter 3. Generalized Second-Order Parametric Optimality Conditions (pp. 93-124)

Chapter 4. Generalized Higher Order (ö, ç, ù, æ, ñ, è, m)-Invexities (pp. 125-148)

Chapter 5. Hybrid Parametric Duality Models (pp. 149-196)

Chapter 6. Hybrid Classes of Duality Models in Discrete Minmax Fractional Programming (pp. 197-242)

Chapter 7. Hanson-Antczak-type Generalized V-Invexity (pp. 243-276)

Bibliography (pp. 277-298)

About the Authors (pp. 299-302)

Index (pp. 303)

Chapter 1

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Chapter 2

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Chapter 4

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Chapter 7

[1] Zalmai, G. J. (2013), Hanson-Antczak-type generalized ( , , , , , ,
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Part II : First-order parametric duality models, Advances in Nonlinear
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Nonlinear Variational Inequalities, 16 (2), 91-126.
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)-V-invex functions in semiinfinite multiobjective fractional programming,
Part I : sufficient efficiency conditions, Advances in Nonlinear
Variational Inequalities, 16 (1), 91-114.

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