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Generalizations of the classical concept of a convex function have
been proposed in various fields such as economics, management
science, engineering, statistics and applied sciences during the
second half of this century. In addition to new results in more
established areas of generalized convexity, this book presents
several important developments in recently emerging areas. Also, a
number of interesting applications are reported.
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Generalized Convexity and Fractional Programming with Economic Applications - Proceedings of the International Workshop on "Generalized Concavity, Fractional Programming and Economic Applications" Held at the University of Pisa, Italy, May 30 - June 1, 1988 (Paperback, Softcover reprint of the original 1st ed. 1990)
Alberto Cambini, Erio Castagnoli, Laura Martein, Piera Mazzoleni, Siegfried Schaible
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R2,989
Discovery Miles 29 890
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Ships in 10 - 15 working days
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Generalizations of convex functions have been used in a variety of
fields such as economics. business administration. engineering.
statistics and applied sciences.. In 1949 de Finetti introduced one
of the fundamental of generalized convex functions characterized by
convex level sets which are now known as quasiconvex functions.
Since then numerous types of generalized convex functions have been
defined in accordance with the need of particular applications.. In
each case such functions preserve soine of the valuable properties
of a convex function. In addition to generalized convex functions
this volume deals with fractional programs. These are constrained
optimization problems which in the objective function involve one
or several ratios. Such functions are often generalized convex.
Fractional programs arise in management science. economics and
numerical mathematics for example. In order to promote the
circulation and development of research in this field. an
international workshop on "Generalized Concavity. Fractional
Programming and Economic Applications" was held at the University
of Pisa. Italy. May 30 - June 1. 1988. Following conferences on
similar topics in Vancouver. Canada in 1980 and in Canton. USA in
1986. it was the first such conference organized in Europe. It
brought together 70 scientists from 11 countries. Organizers were
Professor A. Cambini. University of Pisa. Professor E. Castagnoli.
Bocconi University. Milano. Professor L. Martein. University of
Pisa. Professor P. Mazzoleni. University of Verona and Professor S.
Schaible. University of California. Riverside."
Originally published in 1988, this enduring text remains the most
comprehensive book on generalized convexity and concavity. The
authors present generalized concave functions in a unified
framework, exploring them primarily from the domains of
optimization and economics. Concavity of a function is a common
property used in most of the important theorems concerning
properties of optimization problems in mathematical economics,
operations research, mathematical programming, engineering, and
management science. Generalized concavity deals with the many
nonconcave functions that have properties similar to those of
concave functions. Specific topics covered in this book include:a
review of concavity and the basics of generalized concavity;
applications of generalized concavity to economics; special
function forms such as composite forms, products, ratios, and
quadratic functions; fractional programming; and concave
transformable functions.
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