Description
Convex Optimization: algorithms and complexity
Foundations and Trends in Machine Learning Series, Vol. 8:3-4
Author: BUBECK Sébastien
Language: EnglishSubject for Convex Optimization: algorithms and complexity:
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Publication date: 02-2016
131 p. · Paperback
131 p. · Paperback
Description
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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.
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.
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