Introduction to Online Convex Optimization, second edition
Introduction to Online Convex Optimization, second edition

Author: Elad Hazan

Publisher: MIT Press

Published: 2022-09-06

Total Pages: 249

ISBN-13: 0262046989

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New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process. In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features: Thoroughly updated material throughout New chapters on boosting, adaptive regret, and approachability and expanded exposition on optimization Examples of applications, including prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training, offered throughout Exercises that guide students in completing parts of proofs

Introduction to Online Convex Optimization, second edition
Introduction to Online Convex Optimization, second edition

Author: Elad Hazan

Publisher: MIT Press

Published: 2022-09-06

Total Pages: 249

ISBN-13: 0262370123

DOWNLOAD EBOOK

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process. In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features: Thoroughly updated material throughout New chapters on boosting, adaptive regret, and approachability and expanded exposition on optimization Examples of applications, including prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training, offered throughout Exercises that guide students in completing parts of proofs

Convex Optimization
Convex Optimization

Author: Stephen P. Boyd

Publisher: Cambridge University Press

Published: 2004-03-08

Total Pages: 744

ISBN-13: 9780521833783

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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.

Lectures on Convex Optimization
Lectures on Convex Optimization

Author: Yurii Nesterov

Publisher: Springer

Published: 2018-11-19

Total Pages: 603

ISBN-13: 3319915789

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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.

An Introduction to Optimization
An Introduction to Optimization

Author: Edwin K. P. Chong

Publisher: John Wiley & Sons

Published: 2004-04-05

Total Pages: 497

ISBN-13: 0471654000

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A modern, up-to-date introduction to optimization theory and methods This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Convex Optimization Algorithms
Convex Optimization Algorithms

Author: Dimitri Bertsekas

Publisher: Athena Scientific

Published: 2015-02-01

Total Pages: 576

ISBN-13: 1886529280

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This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.

Online Learning and Online Convex Optimization
Online Learning and Online Convex Optimization

Author: Shai Shalev-Shwartz

Publisher: Foundations & Trends

Published: 2012

Total Pages: 88

ISBN-13: 9781601985460

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Online Learning and Online Convex Optimization is a modern overview of online learning. Its aim is to provide the reader with a sense of some of the interesting ideas and in particular to underscore the centrality of convexity in deriving efficient online learning algorithms.

Algorithms for Convex Optimization
Algorithms for Convex Optimization

Author: Nisheeth K. Vishnoi

Publisher: Cambridge University Press

Published: 2021-10-07

Total Pages: 314

ISBN-13: 1108633994

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In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition
Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition

Author: Michel C. Delfour

Publisher: SIAM

Published: 2019-12-19

Total Pages: 446

ISBN-13: 1611975964

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This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice René Fréchet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical differential calculus, including the chain rule, making it a natural framework for initiating a large audience of undergraduates and non-mathematicians into the world of nondifferentiable optimization. Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition builds upon its prior edition’s foundations in Hadamard semidifferential calculus, showcasing new material linked to convex analysis and nonsmooth optimization. It presents a modern treatment of optimization and Hadamard semidifferential calculus while remaining at a level that is accessible to undergraduate students, and challenges students with exercises related to problems in such fields as engineering, mechanics, medicine, physics, and economics. Answers are supplied in Appendix B. Students of mathematics, physics, engineering, economics, and other disciplines that demand a basic knowledge of mathematical analysis and linear algebra will find this a fitting primary or companion resource for their studies. This textbook has been designed and tested for a one-term course at the undergraduate level. In its full version, it is appropriate for a first-year graduate course and as a reference.

Optimization for Machine Learning
Optimization for Machine Learning

Author: Suvrit Sra

Publisher: MIT Press

Published: 2012

Total Pages: 509

ISBN-13: 026201646X

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An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.