Nonlinear Conjugate Gradient Methods for Unconstrained Optimization. 1st ed. 2020

種類:

電子ブック

責任表示:

by Neculai Andrei

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Andrei, Neculai.
• SpringerLink (Online service)

シリーズ名:

Springer Optimization and Its Applications ; 158

ISBN:

9783030429508 [3030429504]    

注記:

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 metho

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