Convex Optimization: Algorithms and Complexity - Couverture souple

Bubeck, Sébastien

Couverture souple

ISBN 10 : 1601988605 ISBN 13 : 9781601988607

Editeur : now publishers Inc, 2015

Synopsis

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.

Détails de l'édition

• Éditeur: now publishers Inc
• Date d'édition: 2015
• Langue: anglais
• ISBN 10: 1601988605
• ISBN 13: 9781601988607
• Reliure: Broché
• Nombre de pages: 142
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible