Numerical Optimization with Computational Errors

• Main Author: Zaslavski, Alexander J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Springer Optimization and Its Applications, 108
• Subjects: Mathematics.; Numerical analysis.; Calculus of variations.; Operations research.; Management science.; Calculus of Variations and Optimal Control; Optimization.; Numerical Analysis.; Operations Research, Management Science.

This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates...

Table of Contents:

• 1. Introduction
• 2. Subgradient Projection Algorithm
• 3. The Mirror Descent Algorithm
• 4. Gradient Algorithm with a Smooth Objective Function
• 5. An Extension of the Gradient Algorithm
• 6. Weiszfeld's Method
• 7. The Extragradient Method for Convex Optimization
• 8. A Projected Subgradient Method for Nonsmooth Problems
• 9. Proximal Point Method in Hilbert Spaces
• 10. Proximal Point Methods in Metric Spaces
• 11. Maximal Monotone Operators and the Proximal Point Algorithm
• 12. The Extragradient Method for Solving Variational Inequalities
• 13. A Common Solution of a Family of Variational Inequalities
• 14. Continuous Subgradient Method
• 15. Penalty Methods
• 16. Newton's method
• References
• Index. .