First-Order Methods for Convex Optimization

First-order methods for solving convex optimization problems have been at the forefront of mathematical in last 20 years. The rapid development this important class algorithms is motivated by success stories reported various applications, including most importantly machine learning, signal processing, imaging and control theory. potential to provide low accuracy solutions computational complexity which makes them an attractive set tools large-scale problems. In survey, we cover a number key developments gradient-based methods. This includes non-Euclidean extensions classical proximal gradient method, its accelerated versions. Additionally survey recent within projection-free methods, versions primal-dual schemes. We give complete proofs results, highlight unifying aspects several algorithms.