國立虎尾科技大學 |

Numerical Optimization with Computational Errors

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Numerical Optimization with Computational Errors/ by Alexander J. Zaslavski.
作者:	Zaslavski, Alexander J.
面頁冊數:	IX, 304 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Calculus of variations. -
電子資源:	https://doi.org/10.1007/978-3-319-30921-7
ISBN:	9783319309217

Numerical Optimization with Computational Errors
Zaslavski, Alexander J.

Numerical Optimization with Computational Errors[electronic resource] /by Alexander J. Zaslavski. - 1st ed. 2016. - IX, 304 p.online resource. - Springer Optimization and Its Applications,1081931-6828 ;. - Springer Optimization and Its Applications,104.

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

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

527927
Calculus of variations.

LC Class. No.: QA315-316

Dewey Class. No.: 515.64

Numerical Optimization with Computational Errors
LDR:03226nam a22004335i 4500 001 974934
003 DE-He213
005 20200706200403.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319309217 $9 978-3-319-30921-7
024 7 $a 10.1007/978-3-319-30921-7 $2 doi
035 $a 978-3-319-30921-7
050 4 $a QA315-316
050 4 $a QA402.3
072 7 $a PBKQ $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a PBKQ $2 thema
072 7 $a PBU $2 thema
082 0 4 $a 515.64 $2 23
100 1 $a Zaslavski, Alexander J. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1022503
245 1 0 $a Numerical Optimization with Computational Errors $h [electronic resource] / $c by Alexander J. Zaslavski.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a IX, 304 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Optimization and Its Applications, $x 1931-6828 ; $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 Calculus of variations. $3 527927
650 0 $a Numerical analysis. $3 527939
650 0 $a Operations research. $3 573517
650 0 $a Management science. $3 719678
650 1 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Numerical Analysis. $3 671433
650 2 4 $a Operations Research, Management Science. $3 785065
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319309200
776 0 8 $i Printed edition: $z 9783319309224
776 0 8 $i Printed edition: $z 9783319809175
830 0 $a Springer Optimization and Its Applications, $x 1931-6828 ; $v 104 $3 1255232
856 4 0 $u https://doi.org/10.1007/978-3-319-30921-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)