Generalized Fractional Programming
This monograph presents smooth and unified generalized fractional programming (or a program with finite constraints). Under the current interdisciplinary computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of their 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 and 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 robots are about to revolutionize assembly plants forever among all industries, especially the automobile industry. That would also change the face of other industries toward rapid technological innovation.
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 into some generalized fractional programming problems.
Consider fractional programs that arise from management decision science; by analyzing system efficiency in an economic 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 this monograph uniquely presenting 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 by using a new class of multi-time, multi-objective, and variational problems.