Algorithms for convex optimization
著者
書誌事項
Algorithms for convex optimization
Cambridge University Press, 2021
- : pbk
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注記
Includes bibliographical references (p. 310-318) and index
内容説明・目次
内容説明
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.
目次
- 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.
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