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200702s2020 sz ob 001 0 eng d |
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1 |
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|a Andrei, Neculai.
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245 |
1 |
0 |
|a Nonlinear conjugate gradient methods for unconstrained optimization /
|c Neculai Andrei.
|
260 |
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|a Cham :
|b Springer,
|c 2020.
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300 |
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|a 1 online resource.
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336 |
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|a text
|b txt
|2 rdacontent
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490 |
1 |
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|a Springer optimization and its applications,
|x 1931-6828 ;
|v v. 158
|
504 |
|
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|a Includes bibliographical references and indexes.
|
505 |
0 |
0 |
|a Machine generated contents note:
|g 1.
|t Introduction: Overview of Unconstrained Optimization --
|g 1.1.
|t Problem --
|g 1.2.
|t Line Search --
|g 1.3.
|t Optimality Conditions for Unconstrained Optimization --
|g 1.4.
|t Overview of Unconstrained Optimization Methods --
|g 1.4.1.
|t Steepest Descent Method --
|g 1.4.2.
|t Newton Method --
|g 1.4.3.
|t Quasi-Newton Methods --
|g 1.4.4.
|t Modifications of the BFGS Method --
|g 1.4.5.
|t Quasi-Newton Methods with Diagonal Updating of the Hessian --
|g 1.4.6.
|t Limited-Memory Quasi-Newton Methods --
|g 1.4.7.
|t Truncated Newton Methods --
|g 1.4.8.
|t Conjugate Gradient Methods --
|g 1.4.9.
|t Trust-Region Methods --
|g 1.4.10.
|t p-Regularized Methods --
|g 1.5.
|t Test Problems and Applications --
|g 1.6.
|t Numerical Experiments --
|t Notes and References --
|g 2.
|t Linear Conjugate Gradient Algorithm --
|g 2.1.
|t Line Search --
|g 2.2.
|t Fundamental Property of the Line Search Method with Conjugate Directions --
|g 2.3.
|t Linear Conjugate Gradient Algorithm --
|g 2.4.
|t Convergence Rate of the Linear Conjugate Gradient Algorithm --
|g 2.5.
|t Comparison of the Convergence Rate of the Linear Conjugate Gradient and of the Steepest Descent --
|g 2.6.
|t Preconditioning of the Linear Conjugate Gradient Algorithms --
|t Notes and References --
|g 3.
|t General Convergence Results for Nonlinear Conjugate Gradient Methods --
|g 3.1.
|t Types of Convergence --
|g 3.2.
|t Concept of Nonlinear Conjugate Gradient --
|g 3.3.
|t General Convergence Results for Nonlinear Conjugate Gradient Methods --
|g 3.3.1.
|t Convergence Under the Strong Wolfe Line Search --
|g 3.3.2.
|t Convergence Under the Standard Wolfe Line Search --
|g 3.4.
|t Criticism of the Convergence Results --
|t Notes and References --
|g 4.
|t Standard Conjugate Gradient Methods --
|g 4.1.
|t Conjugate Gradient Methods with
|2 in the Numerator of βk --
|g 4.2.
|t Conjugate Gradient Methods with gtk+ 1yk in the Numerator of βk --
|g 4.3.
|t Numerical Study --
|t Notes and References --
|g 5.
|t Acceleration of Conjugate Gradient Algorithms --
|g 5.1.
|t Standard Wolfe Line Search with Cubic Interpolation --
|g 5.2.
|t Acceleration of Nonlinear Conjugate Gradient Algorithms --
|g 5.3.
|t Numerical Study --
|t Notes and References --
|g 6.
|t Hybrid and Parameterized Conjugate Gradient Methods --
|g 6.1.
|t Hybrid Conjugate Gradient Methods Based on the Projection Concept --
|g 6.2.
|t Hybrid Conjugate Gradient Methods as Convex Combinations of the Standard Conjugate Gradient Methods --
|g 6.3.
|t Parameterized Conjugate Gradient Methods --
|t Notes and References --
|g 7.
|t Conjugate Gradient Methods as Modifications of the Standard Schemes --
|g 7.1.
|t Conjugate Gradient with Dai and Liao Conjugacy Condition (DL) --
|g 7.2.
|t Conjugate Gradient with Guaranteed Descent (CG-DESCENT) --
|g 7.3.
|t Conjugate Gradient with Guaranteed Descent and Conjugacy Conditions and a Modified Wolfe Line Search (DESCON) --
|t Notes and References --
|g 8.
|t Conjugate Gradient Methods Memoryless BFGS Preconditioned --
|g 8.1.
|t Conjugate Gradient Memoryless BFGS Preconditioned (CONMIN) --
|g 8.2.
|t Scaling Conjugate Gradient Memoryless BFGS Preconditioned (SCALCG) --
|g 8.3.
|t Conjugate Gradient Method Closest to Scaled Memoryless BFGS Search Direction (DK/CGOPT) --
|g 8.4.
|t New Conjugate Gradient Algorithms Based on Self-Scaling Memoryless BFGS Updating --
|t Notes and References --
|g 9.
|t Three-Term Conjugate Gradient Methods --
|g 9.1.
|t Three-Term Conjugate Gradient Method with Descent and Conjugacy Conditions (TTCG) --
|g 9.2.
|t Three-Term Conjugate Gradient Method with Subspace Minimization (TTS) --
|g 9.3.
|t Three-Term Conjugate Gradient Method with Minimization of One-Parameter Quadratic Model of Minimizing Function (TTDES) --
|t Notes and References --
|g 10.
|t Preconditioning of the Nonlinear Conjugate Gradient Algorithms --
|g 10.1.
|t Preconditioners Based on Diagonal Approximations to the Hessian --
|g 10.2.
|t Criticism of Preconditioning the Nonlinear Conjugate Gradient Algorithms --
|t Notes and References --
|g 11.
|t Other Conjugate Gradient Methods --
|g 11.1.
|t Eigenvalues Versus Singular Values in Conjugate Gradient Algorithms (CECG and SVCG) --
|g 11.2.
|t Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions (CGSYS) --
|g 11.3.
|t Combination of Conjugate Gradient with Limited-Memory BFGS Methods --
|g 11.4.
|t Conjugate Gradient with Subspace Minimization Based on Regularization Model of the Minimizing Function --
|t Notes and References --
|g 12.
|t Discussions, Conclusions, and Large-Scale Optimization --
|t Notes and References.
|
533 |
|
|
|a Electronic reproduction.
|b Ann Arbor, MI
|n Available via World Wide Web.
|
650 |
|
0 |
|a Conjugate gradient methods.
|
650 |
|
0 |
|a Constrained optimization.
|
710 |
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|c Original
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|v v. 158.
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