The Projected Subgradient Algorithm in Convex Optimization (SpringerBriefs in Optimization) - Softcover

Buch 38 von 43: SpringerBriefs in Optimization

Zaslavski, Alexander J.

 
9783030602994: The Projected Subgradient Algorithm in Convex Optimization (SpringerBriefs in Optimization)
Softcover
ISBN 10: 3030602990 ISBN 13: 9783030602994
Verlag: Springer, 2020

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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

Von der hinteren Coverseite

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.

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Verlag
Springer
Erscheinungsdatum
2020
Sprache
Englisch
ISBN 10 
3030602990
ISBN 13 
9783030602994
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
152
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