1# Library to Find Best eBook for Read
Author : Zhenzhen Li
Release : 2020
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Nonconvex Optimization for Low-rank Matrix Related Problems by : Zhenzhen Li
Download or read book Nonconvex Optimization for Low-rank Matrix Related Problems written by Zhenzhen Li. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hiroshi Konno
Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 984/5 ( reviews)
Book Synopsis Optimization on Low Rank Nonconvex Structures by : Hiroshi Konno
Download or read book Optimization on Low Rank Nonconvex Structures written by Hiroshi Konno. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: Global optimization is one of the fastest developing fields in mathematical optimization. In fact, an increasing number of remarkably efficient deterministic algorithms have been proposed in the last ten years for solving several classes of large scale specially structured problems encountered in such areas as chemical engineering, financial engineering, location and network optimization, production and inventory control, engineering design, computational geometry, and multi-objective and multi-level optimization. These new developments motivated the authors to write a new book devoted to global optimization problems with special structures. Most of these problems, though highly nonconvex, can be characterized by the property that they reduce to convex minimization problems when some of the variables are fixed. A number of recently developed algorithms have been proved surprisingly efficient for handling typical classes of problems exhibiting such structures, namely low rank nonconvex structures. Audience: The book will serve as a fundamental reference book for all those who are interested in mathematical optimization.
Author : Christopher Dale White
Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Optimality Guarantees for Non-convex Low Rank Matrix Recovery Problems by : Christopher Dale White
Download or read book Optimality Guarantees for Non-convex Low Rank Matrix Recovery Problems written by Christopher Dale White. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: Low rank matrices lie at the heart of many techniques in scientific computing and machine learning. In this thesis, we examine various scenarios in which we seek to recover an underlying low rank matrix from compressed or noisy measurements. Specifically, we consider the recovery of a rank r positive semidefinite matrix XX[superscript T] [element] R[superscript n x n] from m scalar measurements of the form [mathematic equation] via minimization of the natural l2 loss function [mathematic equation]; we also analyze the quadratic nonnegative matrix factorization (QNMF) approach to clustering where the matrix to be factorized is the transition matrix for a reversible Markov chain. In all of these instances, the optimization problem we wish to solve has many local optima and is highly non-convex. Instead of analyzing convex relaxations, which tend to be complicated and computationally expensive, we operate directly on the natural non-convex problems and prove both local and global optimality guarantees for a family of algorithms.
Author : Prateek Jain
Release : 2017-12-04
Genre : Machine learning
Kind : eBook
Book Rating : 683/5 ( reviews)
Book Synopsis Non-convex Optimization for Machine Learning by : Prateek Jain
Download or read book Non-convex Optimization for Machine Learning written by Prateek Jain. This book was released on 2017-12-04. Available in PDF, EPUB and Kindle. Book excerpt: Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equips the reader with the tools and techniques needed to apply and analyze simple but powerful procedures for non-convex problems. Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. The monograph initiates the discussion with entire chapters devoted to presenting a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. The monograph concludes with a look at four interesting applications in the areas of machine learning and signal processing, and exploring how the non-convex optimization techniques introduced earlier can be used to solve these problems. The monograph also contains, for each of the topics discussed, exercises and figures designed to engage the reader, as well as extensive bibliographic notes pointing towards classical works and recent advances. Non-convex Optimization for Machine Learning can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.
Author : P.-A. Absil
Release : 2009-04-11
Genre : Mathematics
Kind : eBook
Book Rating : 249/5 ( reviews)
Book Synopsis Optimization Algorithms on Matrix Manifolds by : P.-A. Absil
Download or read book Optimization Algorithms on Matrix Manifolds written by P.-A. Absil. This book was released on 2009-04-11. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
