New Trends in Fractional Programming

Ram U. Verma
International Publications USA, Mathematical Sciences Division, Denton, TX, USA

Series: Mathematics Research Developments
BISAC: MAT029000



Volume 10

Issue 1

Volume 2

Volume 3

Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick


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This monograph presents smooth, unified, and generalized fractional programming problems, particularly advanced duality models for discrete min-max fractional programming. In the current, interdisciplinary, computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of their multi-faceted applications including problems ranging from robotics to money market portfolio management.

The other more significant aspect of this monograph is in its consideration of minimax fractional integral type problems using higher order sonvexity and sounivexity notions. This is significant for the development of different types of duality models in terms of weak, strong, and strictly converse duality theorems, which can be handled by transforming them into generalized fractional programming problems.

Fractional integral type programming is one of the fastest expanding areas of optimization, which feature several types of real-world problems. It can be applied to different branches of engineering (including multi-time multi-objective mechanical engineering problems) as well as to economics, to minimize a ratio of functions between given periods of time. Furthermore, it can be utilized as a resource in order to measure the efficiency or productivity of a system. In these types of problems, the objective function is given as a ratio of functions. For example, we consider a problem that deals with minimizing a maximum of several time-dependent ratios involving integral expressions.
(Imprint: Nova)


Chapter 1. Advanced Parameter-Free Duality Models

Chapter 2. Hybrid Duality Models

Chapter 3. New Parametric Duality Models

Chapter 4. Fractional Integral Type Programming

Chapter 5. Integral Type Programming

Chapter 6. Generalized Fractional Integral Programming

General References


“The author in his six chapters of this book presents a very well thought of study of, in particular smooth and unified generalized programming problems. See for example Problem (P). Numerous study cases are presented involving convexity and non-convexity, specializations of which reduce to earlier results by the author or others. The material is very elegantly presented. It is highly recommended to researchers and practitioners who will find it very readable and useful for their research. Parts of this book can also be used in seminars for graduate students as well as senior undergraduate students with interests in this area of research. The bibliography is very informed and updated which makes the book also a great reference source.” - Professor Dr. Ioannis K. Argyros, Cameron University, Department of, Mathematical Sciences, Lawton, OK, USA

Keywords: New Trends, Fractional Programming

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