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.
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 2022-05-31. An Easy Path to Convex Analysis and Applications available in PDF, EPUB and Kindle. Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.
A Simple Path to Convex Analysis and Applications
A Simple 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 A Simple Path to Convex Analysis and Applications write by Boris S. Mordukhovich. This book was released on 2014. A Simple Path to Convex Analysis and Applications available in PDF, EPUB and Kindle. Annotation Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.
Convex Analysis and Beyond
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.
The Projected Subgradient Algorithm in Convex Optimization
The Projected Subgradient Algorithm in Convex Optimization - 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 The Projected Subgradient Algorithm in Convex Optimization write by Alexander J. Zaslavski. This book was released on 2020-11-25. The Projected Subgradient Algorithm in Convex Optimization available in PDF, EPUB and Kindle. This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.
