Last edited by Gardakasa
Wednesday, August 12, 2020 | History

5 edition of Convex functions found in the catalog. # Convex functions

## by Jonathan M. Borwein

Written in English

Subjects:
• Geometry, Non-Euclidean,
• Convex functions,
• Banach spaces

• Edition Notes

Includes bibliographical references and index.

Classifications The Physical Object Statement Jonathan M. Borwein, Jon D. Vanderwerff Series Encyclopedia of mathematics and its applications -- 109 Contributions Vanderwerff, Jon D. LC Classifications QA331.5 .B67 2010 Pagination x, 521 p. Number of Pages 521 Open Library OL27027358M ISBN 10 0521850053 ISBN 10 9780521850056 OCLC/WorldCa 434562716

A convex function f(x) is a real-valued function defined over a convex set X in a vector space such that for any two points x, y in the set and for any λ with ≤ ≤, (+ (−)) ≤ + (−) ().NB: Because X is convex: (+ (−)) must be in X. If the function -f(x) is convex, f(x) is said to ba a concave is easily seen that if a function is both convex and concave, it must be linear. - Definitions of convex functions can be found in the book of R.T. Rockafellar, "Convex Analysis" or in the recommended book by S. Boyd and L. Vandenbergh "Convex optimization".

Purchase Convex Functions, Partial Orderings, and Statistical Applications - 1st Edition. Print Book & E-Book. ISBN , The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in .

The recognition of J-convex functions as a class of functions to be studied is generally traced to Jensen, but as is usually the case, earlier work can be cited that anticipated what was to Size: KB.   Without a doubt Boyd & Vandenberghe is the standard introduction at the graduate level. Anybody who’s serious about understanding convex optimization must engage with it. However, it’s a fairly difficult book, and you have to have a pretty good ma.

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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 applications.

3 Convex functions 67 This book is meant to be Convex functions book in between, a book on general convex optimization that focuses on problem formulation and modeling.

We should also mention what this book is not. It is not a text primarily about convex analysis, or the mathematics of convex optimization; several existing texts. 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.

- Buy Convex Functions and Their Applications: A Contemporary Approach (CMS Books in Mathematics) book online at best prices in India on Read Convex Functions and Their Applications: A Contemporary Approach (CMS Books in Mathematics) book reviews & author details and more at Free delivery on Author: Constantin P.

Niculescu, Lars-Erik Persson. convex functions is too simple for further serious considerations, similar phenomena of “discreteness in direction” occur in nontrivial ways for L-convex or M-convex functions, as we see in x We now go on to the second issue of duality and conjugacy.

For a function f (not necessarily convex), the convex conjugate f†: Rn. R[f+1g is File Size: KB. "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 cturer: Springer. Among its features, the book: develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar.

provides a geometric, highly visual treatment of convex optimization problems, including duality, existence of solutions, and optimality conditions. When speaking about convex functions, it is extremely convenient to think that the func-tion outside its domain also has a value, namely, takes the value +1; with this convention, we can say that.

56 LECTURE 3. CONVEX FUNCTIONS a convex function fon Rn is a function taking values in the extended real axis R[f+1gFile Size: KB. The costs are modeled as bounded convex functions over K. The OCO framework can be seen as a structured repeated game.

The protocol of this learning framework is as follows: At iteration t, the online player chooses x t 2K. After the player has committed to this choice, a convex cost function f t2F: K7!R is revealed.

Geometry of convex functions The link between convex sets and convex functions is via the epigraph: A function is convex if and only if its epigraph is a convex set. −Werner Fenchel We limit our treatment of multidimensional functions to ﬁnite-dimensional Euclidean space.

Then an icon for a one-dimensional (real) convex function is bowl.This book aims at an accessible, concise, and intuitive exposition of two related subjects that ﬁnd broad practical application: (a) Convex analysis, particularly as it relates to Size: 6MB.2 MARKUS GRASMAIR Remark 3.

There is a very close connection between convex sets and convex functions: One can show that a function f: Rn!R is convex, if and only if the so-called epigraph of f, which is the subset of Rn R consisting of all points (x;t) with t f(x), is a convex set.