by Ram U. Verma
Part of the Infosys Science Foundation Series in Mathematical Sciences Series
This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.
|Publication date:||3rd November 2017|
|Author:||Ram U. Verma|
|Publisher:||Springer Verlag, Singapore|
|Categories:||Optimization, Probability & statistics, Economic theory & philosophy,|
RAM U. VERMA is president of International Publications, USA. Before joining Texas State University, he held several academic positions, ranging from lecturer to assistant professor, associate professor, and full professor at the University of Cape Coast, the University of Tripoli, the University of Orient, the University of Puerto Rico, New York University (visiting faculty), the University of Central Florida, Mount Olive College, Duke University (visiting scholar) and the University of Toledo. His research interests encompass mathematical programming, fractional programming, semi-infinite fractional programming, multi-objective fractional programming, numerical analysis, generalised Newton's methods, new generation Newton-type methods, nonlinear functional analysis, applied analysis, evolution ...More About Ram U. Verma