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 that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative.
This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton's method.
Reviews / Votes
"The author 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. Researchers and students will find this book instructive and informative. The book has contains 16 chapters . ." (Hans Benker, zbMATH 1347.65112, 2016)
Series
Edition
Softcover reprint of the original 1st ed. 2016
Language
Place of publication
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
ISBN-13
978-3-319-80917-5 (9783319809175)
DOI
10.1007/978-3-319-30921-7
Schweitzer Classification
¿Alexander J. Zaslavski is professor in the Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. He has authored numerous books with Springer, the most recent of which include Turnpike Theory for the Robinson-Solow-Srinivasan Model (978-3-030-60306-9), The Projected Subgradient Algorithm in Convex Optimization (978-3-030-60299-4), Convex Optimization with Computational Errors (978-3-030-37821-9), Turnpike Conditions in Infinite Dimensional Optimal Control (978-3-030-20177-7), Optimization on Solution Sets of Common Fixed Point Problems (978-3-030-78848-3).
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.
