國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁 到查詢結果 [ author_sort:"andrei, neculai." ]

切換: 標籤 | MARC模式 | ISBD

Nonlinear conjugate gradient methods...

Andrei, Neculai.

Nonlinear conjugate gradient methods for unconstrained optimization

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlinear conjugate gradient methods for unconstrained optimizationby Neculai Andrei.
作者:	Andrei, Neculai.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xxviii, 498 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Conjugate gradient methods.
電子資源:	https://doi.org/10.1007/978-3-030-42950-8
ISBN:	9783030429508$q(electronic bk.)

Nonlinear conjugate gradient methods for unconstrained optimization
Andrei, Neculai.

Nonlinear conjugate gradient methods for unconstrained optimization[electronic resource] /by Neculai Andrei. - Cham :Springer International Publishing :2020. - xxviii, 498 p. :ill., digital ;24 cm. - Springer optimization and its applications,v.1581931-6828 ;. - Springer optimization and its applications ;v. 3..

1. Introduction -- 2. Linear Conjugate Gradient Algorithm -- 3. General Convergence Results for Nonlinear Conjugate Gradient Methods -- 4. Standard Conjugate Gradient Methods -- 5. Acceleration of Conjugate Gradient Algorithms -- 6. Hybrid and Parameterized Conjugate Gradient Methods -- 7. Conjugate Gradient Methods as Modifications of the Standard Schemes -- 8. Conjugate Gradient Methods Memoryless BFGS Preconditioned -- 9. Three-Term Conjugate Gradient Methods -- 10. Other Conjugate Gradient Methods -- 11. Discussion and Conclusions -- References -- Author Index -- Subject Index.

Two approaches are known for solving large-scale unconstrained optimization problems-the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

ISBN: 9783030429508$q(electronic bk.)

Standard No.: 10.1007/978-3-030-42950-8doiSubjects--Topical Terms:

184269
Conjugate gradient methods.

LC Class. No.: QA218 / .A537 2020

Dewey Class. No.: 512.94

Nonlinear conjugate gradient methods for unconstrained optimization
LDR:03779nmm a2200337 a 4500 001 580603
003 DE-He213
005 20201029134333.0
006 m
007 cr
008 210105s2020
020 $a 9783030429508$q(electronic bk.)
020 $a 9783030429492$q(paper)
024 7 $a 10.1007/978-3-030-42950-8 $2 doi
035 $a 978-3-030-42950-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA218 $b .A537 2020
072 7 $a PBU $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 512.94 $2 23
090 $a QA218 $b .A559 2020
100 1 $a Andrei, Neculai. $3 798172
245 1 0 $a Nonlinear conjugate gradient methods for unconstrained optimization $h [electronic resource] / $c by Neculai Andrei.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xxviii, 498 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer optimization and its applications, $x 1931-6828 ; $v v.158
505 0 $a 1. Introduction -- 2. Linear Conjugate Gradient Algorithm -- 3. General Convergence Results for Nonlinear Conjugate Gradient Methods -- 4. Standard Conjugate Gradient Methods -- 5. Acceleration of Conjugate Gradient Algorithms -- 6. Hybrid and Parameterized Conjugate Gradient Methods -- 7. Conjugate Gradient Methods as Modifications of the Standard Schemes -- 8. Conjugate Gradient Methods Memoryless BFGS Preconditioned -- 9. Three-Term Conjugate Gradient Methods -- 10. Other Conjugate Gradient Methods -- 11. Discussion and Conclusions -- References -- Author Index -- Subject Index.
520 $a Two approaches are known for solving large-scale unconstrained optimization problems-the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.
650 0 $a Conjugate gradient methods. $3 184269
650 0 $a Constrained optimization. $3 455920
650 1 4 $a Optimization. $3 274084
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
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 https://doi.org/10.1007/978-3-030-42950-8
950 $a Mathematics and Statistics (Springer-11649)