The Projected Subgradient Algorithm in Convex Optimization

Alexander J. Zaslavski

ISBN 10: 3030602990 / ISBN 13: 9783030602994

Published by Springer International Publishing Nov 2020, 2020

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for di erent steps are di erent, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning. 152 pp. Englisch.

Seller Inventory # 9783030602994

Bibliographic Details

• Title: The Projected Subgradient Algorithm in Convex Optimization
• Publisher: Springer International Publishing Nov 2020
• Publication Date: 2020
• Language: English
• ISBN 10: 3030602990
• ISBN 13: 9783030602994
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 9D millimeters 235 millimeters width by 155 millimeters height by 9 millimeters depth
• Weight: 242 grams

About this title

Synopsis

This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization  to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general.  The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization.  The subgradient  projection algorithm is one of the most important tools in optimization theory and its applications. An optimization  problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different.  This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this.  In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.

About the Author

​Alexander J. Zaslavski is professor in the Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel.​