Author : Boyan Sirakov
Publisher : World Scientific
Page : 5393 pages
File Size : 22,63 MB
Release : 2019-02-27
Category : Mathematics
ISBN : 9813272899
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author : Alain Bensoussan
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 11,26 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662129051
This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.
Author : A. R. Conn
Publisher : SIAM
Page : 960 pages
File Size : 39,16 MB
Release : 2000-01-01
Category : Mathematics
ISBN : 0898714605
Mathematics of Computing -- General.
Author : Alexandre d'Aspremont
Publisher :
Page : 262 pages
File Size : 19,17 MB
Release : 2021-12-15
Category : Technology & Engineering
ISBN : 9781680839289
This monograph covers recent advances in a range of acceleration techniques frequently used in convex optimization. Using quadratic optimization problems, the authors introduce two key families of methods, namely momentum and nested optimization schemes. These methods are covered in detail and include Chebyshev Acceleration, Nonlinear Acceleration, Nesterov Acceleration, Proximal Acceleration and Catalysts and Restart Schemes.This book provides the reader with an in-depth description of the developments in Acceleration Methods since the early 2000s, whilst referring the reader back to underpinning earlier work for further understanding. This topic is important in the modern-day application of convex optimization techniques in many applicable areas.This book is an introduction to the topic that enables the reader to quickly understand the important principles and apply the techniques to their own research.
Author : Yurii Nesterov
Publisher : Springer
Page : 603 pages
File Size : 11,51 MB
Release : 2018-11-19
Category : Mathematics
ISBN : 3319915789
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
Author : Sébastien Bubeck
Publisher : Foundations and Trends (R) in Machine Learning
Page : 142 pages
File Size : 45,1 MB
Release : 2015-11-12
Category : Convex domains
ISBN : 9781601988607
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. It begins with the fundamental theory of black-box optimization and proceeds to guide the reader through recent advances in structural optimization and stochastic optimization. The presentation of black-box optimization, strongly influenced by the seminal book by Nesterov, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. Special attention is also given to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging), and discussing their relevance in machine learning. The text provides a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. It also briefly touches upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.
Author : Jeremy Watt
Publisher : Cambridge University Press
Page : 597 pages
File Size : 32,73 MB
Release : 2020-01-09
Category : Computers
ISBN : 1108480721
An intuitive approach to machine learning covering key concepts, real-world applications, and practical Python coding exercises.
Author : Stephen P. Boyd
Publisher : Cambridge University Press
Page : 744 pages
File Size : 28,89 MB
Release : 2004-03-08
Category : Business & Economics
ISBN : 9780521833783
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.
Author : Amir Beck
Publisher : SIAM
Page : 476 pages
File Size : 11,23 MB
Release : 2017-10-02
Category : Mathematics
ISBN : 1611974984
The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
Author : Arkadiĭ Semenovich Nemirovskiĭ
Publisher : John Wiley & Sons
Page : 412 pages
File Size : 17,90 MB
Release : 1983
Category : Mathematics
ISBN :
