Algorithms for Convex Optimization
Cambridge University Press, 10/7/2021
EAN 9781108482028, ISBN10: 1108482023
Hardcover, 200 pages, 23.4 x 15.8 x 2.7 cm
Language: English
Originally published in English
In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.
1. Bridging continuous and discrete optimization
2. Preliminaries
3. Convexity
4. Convex optimization and efficiency
5. Duality and optimality
6. Gradient descent
7. Mirror descent and multiplicative weights update
8. Accelerated gradient descent
9. Newton's method
10. An interior point method for linear programming
11. Variants of the interior point method and self-concordance
12. Ellipsoid method for linear programming
13. Ellipsoid method for convex optimization.