Название: Algorithms for Convex Optimization
Автор: Nisheeth K. Vishnoi
Издательство: Cambridge University Press
Год: 2021
Страниц: 200
Язык: английский
Формат: epub
Размер: 10.27 MB

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.

The goal of this book is to enable a reader to gain an in-depth understanding of algorithms for convex optimization. The emphasis is to derive key algorithms for convex optimization from first principles and to establish precise running time bounds in terms of the input length. Given the broad applicability of these methods, it is not possible for a single book to show the applications of these methods to all of them. This book shows applications to fast algorithms for various discrete optimization and counting problems. The applications selected in this book serve the purpose of illustrating a rather surprising bridge between continuous and discrete optimization.

The book is self-contained and starts with a review of calculus, linear algebra, geometry, dynamical systems, and graph theory in Chapter 2. Exercises posed in this book not only play an important role in checking one’s understanding; sometimes important methods and concepts are introduced and developed entirely through them. Examples include the Frank-Wolfe method, coordinate descent, stochastic gradient descent, online convex optimization, the min-max theorem for zero-sum games, the Winnow algorithm for classification, bandit optimization, the conjugate gradient method, primal-dual interior point method, and matrix scaling.