Convex Analysis and Beyond - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Analysis and Beyond write by Boris S. Mordukhovich. This book was released on 2022-04-24. Convex Analysis and Beyond available in PDF, EPUB and Kindle. This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
An Easy Path to Convex Analysis and Applications
An Easy Path to Convex Analysis and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Easy Path to Convex Analysis and Applications write by Boris Mordukhovich. This book was released on 2023-06-16. An Easy Path to Convex Analysis and Applications available in PDF, EPUB and Kindle. This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.
Convex Analysis
Convex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Analysis write by R. Tyrrell Rockafellar. This book was released on 1997-01-12. Convex Analysis available in PDF, EPUB and Kindle. Topics treat systems of inequalities; Lagrange multipliers; minimax theorems and duality; structures of convex sets and functions; and more. Available for the first time in paperback, Rockafellar's classic study has firmly established a vital area not only for pure mathematics but also for applications to economics and engineering. Readers will find sound knowledge of linear algebra and introductory real analysis a major benefit to the assimilation of this work.
Lectures On Convex Sets (Second Edition)
Lectures On Convex Sets (Second Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures On Convex Sets (Second Edition) write by Valeriu Soltan. This book was released on 2019-11-28. Lectures On Convex Sets (Second Edition) available in PDF, EPUB and Kindle. The book provides a self-contained and systematic treatment of algebraic and topological properties of convex sets in the n-dimensional Euclidean space. It benefits advanced undergraduate and graduate students with various majors in mathematics, optimization, and operations research. It may be adapted as a primary book or an additional text for any course in convex geometry or convex analysis, aimed at non-geometers. It can be a source for independent study and a reference book for researchers in academia.The second edition essentially extends and revises the original book. Every chapter is rewritten, with many new theorems, examples, problems, and bibliographical references included. It contains three new chapters and 100 additional problems with solutions.
Convex Analysis and Optimization in Hadamard Spaces
Convex Analysis and Optimization in Hadamard Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Convex Analysis and Optimization in Hadamard Spaces write by Miroslav Bacak. This book was released on 2014-10-29. Convex Analysis and Optimization in Hadamard Spaces available in PDF, EPUB and Kindle. In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.
