Siegfried Schaible – författare

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.

This volume contains invited articles and refereed contributions presented at an international workshop held at the University of Pisa in 1988. The subject of the book is generalizations of the classical concept of a convex function. Many of these generalizations are prompted by applications in economics. In addition, special types of generalized convex programmes, namely fractional programmes, are presented. The book is interdisciplinary, and brings together the most recent developments in these fields from mathematics, economics, operations research and management science. It presents the state of the art in the fields of generalized convexity and fractional programming.

Generalizations of the classical concept of a convexfunction have been proposed in various fields such aseconomics, management science, engineering, statistics andapplied sciences during the second half of this century. Inaddition to new results in more established areas ofgeneralized convexity, this book presents several importantdevelopments in recently emerging areas. Also, a number ofinteresting applications are reported.

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.