Nonlinear conjugate gradient methods for unconstrained optimization. (2020)
- Record Type:
- Book
- Title:
- Nonlinear conjugate gradient methods for unconstrained optimization. (2020)
- Main Title:
- Nonlinear conjugate gradient methods for unconstrained optimization
- Further Information:
- Note: Neculai Andrei.
- Other Names:
- Andrei, Neculai
- Contents:
- Intro -- Preface -- Contents -- List of Figures -- List of Tables -- List of Algorithms -- 1 Introduction: Overview of Unconstrained Optimization -- 1.1 The Problem -- 1.2 Line Search -- 1.3 Optimality Conditions for Unconstrained Optimization -- 1.4 Overview of Unconstrained Optimization Methods -- 1.4.1 Steepest Descent Method -- 1.4.2 Newton Method -- 1.4.3 Quasi-Newton Methods -- 1.4.4 Modifications of the BFGS Method -- 1.4.5 Quasi-Newton Methods with Diagonal Updating of the Hessian -- 1.4.6 Limited-Memory Quasi-Newton Methods -- 1.4.7 Truncated Newton Methods 1.4.8 Conjugate Gradient Methods -- 1.4.9 Trust-Region Methods -- 1.4.10 p-Regularized Methods -- 1.5 Test Problems and Applications -- 1.6 Numerical Experiments -- 2 Linear Conjugate Gradient Algorithm -- 2.1 Line Search -- 2.2 Fundamental Property of the Line Search Method with Conjugate Directions -- 2.3 The Linear Conjugate Gradient Algorithm -- 2.4 Convergence Rate of the Linear Conjugate Gradient Algorithm -- 2.5 Comparison of the Convergence Rate of the Linear Conjugate Gradient and of the Steepest Descent -- 2.6 Preconditioning of the Linear Conjugate Gradient Algorithms 4.2 Conjugate Gradient Methods with g_{k {\, +\, } 1} {T} y_{k} in the Numerator of \beta_{k} -- 4.3 Numerical Study -- 5 Acceleration of Conjugate Gradient Algorithms -- 5.1 Standard Wolfe Line Search with Cubic Interpolation -- 5.2 Acceleration of Nonlinear Conjugate Gradient Algorithms -- 5.3 Numerical Study -- 6 Hybrid andIntro -- Preface -- Contents -- List of Figures -- List of Tables -- List of Algorithms -- 1 Introduction: Overview of Unconstrained Optimization -- 1.1 The Problem -- 1.2 Line Search -- 1.3 Optimality Conditions for Unconstrained Optimization -- 1.4 Overview of Unconstrained Optimization Methods -- 1.4.1 Steepest Descent Method -- 1.4.2 Newton Method -- 1.4.3 Quasi-Newton Methods -- 1.4.4 Modifications of the BFGS Method -- 1.4.5 Quasi-Newton Methods with Diagonal Updating of the Hessian -- 1.4.6 Limited-Memory Quasi-Newton Methods -- 1.4.7 Truncated Newton Methods 1.4.8 Conjugate Gradient Methods -- 1.4.9 Trust-Region Methods -- 1.4.10 p-Regularized Methods -- 1.5 Test Problems and Applications -- 1.6 Numerical Experiments -- 2 Linear Conjugate Gradient Algorithm -- 2.1 Line Search -- 2.2 Fundamental Property of the Line Search Method with Conjugate Directions -- 2.3 The Linear Conjugate Gradient Algorithm -- 2.4 Convergence Rate of the Linear Conjugate Gradient Algorithm -- 2.5 Comparison of the Convergence Rate of the Linear Conjugate Gradient and of the Steepest Descent -- 2.6 Preconditioning of the Linear Conjugate Gradient Algorithms 4.2 Conjugate Gradient Methods with g_{k {\, +\, } 1} {T} y_{k} in the Numerator of \beta_{k} -- 4.3 Numerical Study -- 5 Acceleration of Conjugate Gradient Algorithms -- 5.1 Standard Wolfe Line Search with Cubic Interpolation -- 5.2 Acceleration of Nonlinear Conjugate Gradient Algorithms -- 5.3 Numerical Study -- 6 Hybrid and Parameterized Conjugate Gradient Methods -- 6.1 Hybrid Conjugate Gradient Methods Based on the Projection Concept -- 6.2 Hybrid Conjugate Gradient Methods as Convex Combinations of the Standard Conjugate Gradient Methods -- 6.3 Parameterized Conjugate Gradient Methods 7 Conjugate Gradient Methods as Modifications of the Standard Schemes -- 7.1 Conjugate Gradient with Dai and Liao Conjugacy Condition (DL) -- 7.2 Conjugate Gradient with Guaranteed Descent (CG-DESCENT) -- 7.3 Conjugate Gradient with Guaranteed Descent and Conjugacy Conditions and a Modified Wolfe Line Search (DESCON) -- 8 Conjugate Gradient Methods Memoryless BFGS Preconditioned -- 8.1 Conjugate Gradient Memoryless BFGS Preconditioned (CONMIN) -- 8.2 Scaling Conjugate Gradient Memoryless BFGS Preconditioned (SCALCG) … (more)
- Publisher Details:
- Cham : Springer
- Publication Date:
- 2020
- Extent:
- 1 online resource
- Subjects:
- 512.9/4
Conjugate gradient methods
Constrained optimization
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030429508
3030429504 - Related ISBNs:
- 3030429490
9783030429492 - Notes:
- Note: Includes bibliographical references and indexes.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Physical Locations:
- British Library HMNTS - ELD.DS.513379
- Ingest File:
- 03_095.xml