國立高雄大學圖資館 |

Language: English

Back

Numerical optimization with computat...

SpringerLink (Online service)

Numerical optimization with computational errors

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical optimization with computational errorsby Alexander J. Zaslavski.
Author:	Zaslavski, Alexander J.
Published:	Cham :Springer International Publishing :2016.
Description:	ix, 304 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical optimization.
Online resource:	http://dx.doi.org/10.1007/978-3-319-30921-7
ISBN:	9783319309217$q(electronic bk.)

Numerical optimization with computational errors
Zaslavski, Alexander J.

Numerical optimization with computational errors[electronic resource] /by Alexander J. Zaslavski. - Cham :Springer International Publishing :2016. - ix, 304 p. :ill., digital ;24 cm. - Springer optimization and its applications,v.1081931-6828 ;. - Springer optimization and its applications ;v. 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.

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.

ISBN: 9783319309217$q(electronic bk.)

Standard No.: 10.1007/978-3-319-30921-7doiSubjects--Topical Terms:

183292
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Numerical optimization with computational errors
LDR:02836nmm a2200349 a 4500 001 486830
003 DE-He213
005 20161012172553.0
006 m d
007 cr nn 008maaau
008 161116s2016 gw s 0 eng d
020 $a 9783319309217$q(electronic bk.)
020 $a 9783319309200$q(paper)
024 7 $a 10.1007/978-3-319-30921-7 $2 doi
035 $a 978-3-319-30921-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.5
072 7 $a PBKQ $2 bicssc
072 7 $a PBU $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a MAT029020 $2 bisacsh
082 0 4 $a 519.6 $2 23
090 $a QA402.5 $b .Z38 2016
100 1 $a Zaslavski, Alexander J. $3 261260
245 1 0 $a Numerical optimization with computational errors $h [electronic resource] / $c by Alexander J. Zaslavski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a ix, 304 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer optimization and its applications, $x 1931-6828 ; $v v.108
505 0 $a 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.
520 $a 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.
650 0 $a Mathematical optimization. $3 183292
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Numerical Analysis. $3 275681
650 2 4 $a Operations Research, Management Science. $3 511451
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer optimization and its applications ; $v v. 3. $3 440366
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-30921-7
950 $a Mathematics and Statistics (Springer-11649)