This monograph presents the main Complexity theorems in Convex optimization and their corresponding 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..
In stochastic optimization it discusses stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms.
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.
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 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.
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.
This monograph presents the main Complexity theorems in Convex optimization and their corresponding algorithms
