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Convex functions

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Published by Academic Press in New York .
Written in English


  • Convex functions

Book details:

Edition Notes

Bibliography: p. [273]-287.

Statement[by] A. Wayne Roberts [and] Dale E. Varberg.
SeriesPure and applied mathematics; a series of monographs and textbooks ;, 57, Pure and applied mathematics (Academic Press) ;, 57.
ContributionsVarberg, Dale E., joint author.
LC ClassificationsQA3 .P8 vol. 57, QA331.5 .P8 vol. 57
The Physical Object
Paginationxx, 300 p.
Number of Pages300
ID Numbers
Open LibraryOL5291903M
ISBN 100125897405
LC Control Number72012186

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This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach by:   Types of Functions >. A convex function has a very distinct ‘smiley face’ appearance. A line drawn between any two points on the interval will never dip below the graph. It’s more precisely defined as a function where, for every interval on its domain, the midpoint isn’t larger than (higher than) the arithmetic mean of the values (heights) at the ends of the interval. "The book is devoted to elementary theory of convex functions. The book will be useful to all who are interested in convex functions and their applications." (Peter Zabreiko, Zentralblatt MATH, Vol. (2), ) "This is a nice little book, providing a new look at the old subject of convexity and treating it from different points of view.   Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching interests intersect with the field of convexity. It covers a large variety of subjects, from the one .

This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and : Constantin Niculescu, Lars-Erik Persson. Convex, concave, strictly convex, and strongly convex functions First and second order characterizations of convex functions Optimality conditions for convex problems 1 Theory of convex functions De nition Let’s rst recall the de nition of a convex function. De nition 1. A function f: Rn!Ris convex if its domain is a convex set and for File Size: 1MB. means. So are the log-convex functions, the multiplicatively convex functions, the subharmonic functions, and the functions which are convex with respect to a subgroup of the linear group. Our book aims to be a thorough introduction to the contemporary convex functions theory. It covers a large variety of subjects, from one real variable. The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are .

The main result of this chapter is the equivalence between the different definitions of the subdifferential of a convex function, including the proximal one. We finish the chapter with two examples that study the subdifferential of two convex functions: the distance to a convex set, and the maximum function. Convex Functions book. Read reviews from world’s largest community for readers.3/5(1). The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective domain. You can likely see the relevant proof using Amazon's or Google Book. If the functions f and g are convex downward (upward), then any linear combination af+bg where a, b are positive real numbers is also convex downward (upward). If the function u = g(x) is convex downward, and the function y = f(u) is convex downward and non-decreasing, then the composite function y = f(g(x)) is also convex downward.