國立虎尾科技大學 |

Splitting Algorithms, Modern Operator Theory, and Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Splitting Algorithms, Modern Operator Theory, and Applications/ edited by Heinz H. Bauschke, Regina S. Burachik, D. Russell Luke.
其他作者:	Bauschke, Heinz H.
面頁冊數:	XIX, 489 p. 35 illus., 25 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Operator theory. -
電子資源:	https://doi.org/10.1007/978-3-030-25939-6
ISBN:	9783030259396

Splitting Algorithms, Modern Operator Theory, and Applications
Splitting Algorithms, Modern Operator Theory, and Applications[electronic resource] /edited by Heinz H. Bauschke, Regina S. Burachik, D. Russell Luke. - 1st ed. 2019. - XIX, 489 p. 35 illus., 25 illus. in color.online resource.

1. Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions (H. Attouch, J. Peypouquet) -- 2. Constraint Splitting and Projection Methods for Optimal Control of Double Integrator (H.H. Bauschke, R.S. Burachik, C.Y. Kaya) -- 3. Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets (H.,H. Bauschke, S. Gretchko, W.M. Moursi) -- 4. Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators Over Affine Sets (R. I. Bot, E.R. Csetnek, D. Meier) -- 5. Regularization of Ill-posed Problems with Non-Negative Solutions (C. Clason, B. Kaltenbacher, E. Resmerita) -- 6. Characterizations of Super-regularity and its Variants (A. Danillidis, D.R. Luke, M. Tam) -- 7. The Inverse Function Theorems of L.M. Graves (A.L. Dontchev) -- 8. Block-wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-block Convex Programming (X. Fu, B. He, X. Wang, X. Yuan) -- 9. Variable Metric Algorithms Driven by Averaged Operations (L.E. Glaudin) -- 10. A Glimpse at Pointwise Asymptotic Stability for Continuous-time and Discrete-time Dynamics (R. Goebel) -- 11. A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems (S-M Grad) -- 12. Non-polyhedral Extensions of the Frank and Wolfe Theorem (J.E. Martínez-Legaz, D. Noll, W. Sosa) -- 13. A Note on the Equivalence of Operator Splitting Methods (W.M. Moursi, Y. Zinchenko) -- 14. Quasidensity: A Survey and Some Examples (S. Simons) -- 15. On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method (A. Themelis, M. Ahookosh, P. Patrinos) -- 16. Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators - Enhancements of SVM and Lasso (I. Yamada, M. Yamagishi) -- Appendix -- References.

This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

ISBN: 9783030259396

Standard No.: 10.1007/978-3-030-25939-6doiSubjects--Topical Terms:

527910
Operator theory.

LC Class. No.: QA329-329.9

Dewey Class. No.: 515.724

Splitting Algorithms, Modern Operator Theory, and Applications
LDR:04165nam a22003975i 4500 001 1006253
003 DE-He213
005 20200701155006.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783030259396 $9 978-3-030-25939-6
024 7 $a 10.1007/978-3-030-25939-6 $2 doi
035 $a 978-3-030-25939-6
050 4 $a QA329-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.724 $2 23
245 1 0 $a Splitting Algorithms, Modern Operator Theory, and Applications $h [electronic resource] / $c edited by Heinz H. Bauschke, Regina S. Burachik, D. Russell Luke.
250 $a 1st ed. 2019.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a XIX, 489 p. 35 illus., 25 illus. in color. $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
505 0 $a 1. Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions (H. Attouch, J. Peypouquet) -- 2. Constraint Splitting and Projection Methods for Optimal Control of Double Integrator (H.H. Bauschke, R.S. Burachik, C.Y. Kaya) -- 3. Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets (H.,H. Bauschke, S. Gretchko, W.M. Moursi) -- 4. Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators Over Affine Sets (R. I. Bot, E.R. Csetnek, D. Meier) -- 5. Regularization of Ill-posed Problems with Non-Negative Solutions (C. Clason, B. Kaltenbacher, E. Resmerita) -- 6. Characterizations of Super-regularity and its Variants (A. Danillidis, D.R. Luke, M. Tam) -- 7. The Inverse Function Theorems of L.M. Graves (A.L. Dontchev) -- 8. Block-wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-block Convex Programming (X. Fu, B. He, X. Wang, X. Yuan) -- 9. Variable Metric Algorithms Driven by Averaged Operations (L.E. Glaudin) -- 10. A Glimpse at Pointwise Asymptotic Stability for Continuous-time and Discrete-time Dynamics (R. Goebel) -- 11. A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems (S-M Grad) -- 12. Non-polyhedral Extensions of the Frank and Wolfe Theorem (J.E. Martínez-Legaz, D. Noll, W. Sosa) -- 13. A Note on the Equivalence of Operator Splitting Methods (W.M. Moursi, Y. Zinchenko) -- 14. Quasidensity: A Survey and Some Examples (S. Simons) -- 15. On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method (A. Themelis, M. Ahookosh, P. Patrinos) -- 16. Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators - Enhancements of SVM and Lasso (I. Yamada, M. Yamagishi) -- Appendix -- References.
520 $a This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.
650 0 $a Operator theory. $3 527910
650 0 $a Calculus of variations. $3 527927
650 0 $a Partial differential equations. $3 1102982
650 0 $a Functional analysis. $3 527706
650 0 $a Numerical analysis. $3 527939
650 1 4 $a Operator Theory. $3 672127
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Numerical Analysis. $3 671433
700 1 $a Bauschke, Heinz H. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 785983
700 1 $a Burachik, Regina S. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 677320
700 1 $a Luke, D. Russell. $e editor. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1299764
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030259389
776 0 8 $i Printed edition: $z 9783030259402
776 0 8 $i Printed edition: $z 9783030259419
856 4 0 $u https://doi.org/10.1007/978-3-030-25939-6
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)