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• W2154094669 abstract "This monograph presents the main mathematical ideas in convex optimization. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by the seminal book of Nesterov, includes the analysis of the Ellipsoid Method, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, Mirror Descent, and Dual Averaging) and discuss their relevance in machine learning. We provide 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 we discuss Stochastic Gradient Descent, mini-batches, Random Coordinate Descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods." @default.
• W2154094669 created "2016-06-24" @default.
• W2154094669 creator A5021842384 @default.
• W2154094669 date "2014-05-20" @default.
• W2154094669 modified "2023-09-27" @default.
• W2154094669 title "Theory of Convex Optimization for Machine Learning." @default.
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