Convex Functions
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Convex Functions And Their Applications
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Author : Constantin Niculescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-11
Convex Functions And Their Applications written by Constantin Niculescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-11 with Mathematics categories.
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 real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Prékopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming. Many results are new and the whole book reflects the authors’ own experience, both in teaching and research. The 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 for graduate courses.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Convex Functions Monotone Operators And Differentiability
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Author : Robert R. Phelps
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-07-29
Convex Functions Monotone Operators And Differentiability written by Robert R. Phelps and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-29 with Mathematics categories.
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization. While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.
Convex Functions
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Author : Jonathan M. Borwein
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-14
Convex Functions written by Jonathan M. Borwein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
The product of a collaboration of over 15 years, this volume is unique because it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics, treating convex functions in both Euclidean and Banach spaces.
Convex Functions And Their Applications
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Author : Constantin P. Niculescu
language : en
Publisher: Springer
Release Date : 2018-06-08
Convex Functions And Their Applications written by Constantin P. Niculescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-08 with Mathematics categories.
Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Convex Functions
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Author : Jonathan M. Borwein
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-14
Convex Functions written by Jonathan M. Borwein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. 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 spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.
Convex Functions And Optimization Methods On Riemannian Manifolds
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Author : C. Udriste
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Convex Functions And Optimization Methods On Riemannian Manifolds written by C. Udriste and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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 close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.
Convex Functions
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Author :
language : en
Publisher: Academic Press
Release Date : 1974-02-08
Convex Functions written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-02-08 with Mathematics categories.
Convex Functions
Convex Functions Partial Orderings And Statistical Applications
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Author : Josip E. Peajcariaac
language : en
Publisher: Academic Press
Release Date : 1992-06-03
Convex Functions Partial Orderings And Statistical Applications written by Josip E. Peajcariaac and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-03 with Mathematics categories.
This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists. Presents classical and newly published results on convex functions and related inequalities Explains partial ordering based on arrangement and their applications in mathematics, probability, statsitics, and reliability Demonstrates the connection of partial ordering with other well-known orderings such as majorization and Schur functions Will generate further research and applications