Author | Hestenes, Magnus Rudolph. author |
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Title | Conjugate Direction Methods in Optimization [electronic resource] / by Magnus Rudolph Hestenes |
Imprint | New York, NY : Springer New York, 1980 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6048-6 |
Descript | X, 325 p. online resource |
I Newtonโs Method and the Gradient Method -- 1 Introduction -- 2 Fundamental Concepts -- 3 Iterative Methods for Solving g(x) = 0 -- 4 Convergence Theorems -- 5 Minimization of Functions by Newtonโs Method -- 6 Gradient MethodsโThe Quadratic Case -- 7 General Descent Methods -- 8 Iterative Methods for Solving Linear Equations -- 9 Constrained Minima -- II Conjugate Direction Methods -- 1 Introduction -- 2 Quadratic Functions on En -- 3 Basic Properties of Quadratic Functions -- 4 Minimization of a Quadratic Function F on k-Planes -- 5 Method of Conjugate Directions (CD-Method) -- 6 Method of Conjugate Gradients (CG-Algorithm) -- 7 Gradient PARTAN -- 8 CG-Algorithms for Nonquadratic Functions -- 9 Numerical Examples -- 10 Least Square Solutions -- III Conjugate Gram-Schmidt Processes -- 1 Introduction -- 2 A Conjugate Gram-Schmidt Process -- 3 CGS-CG-Algorithms -- 4 A Connection of CGS-Algorithms with Gaussian Elimination -- 5 Method of Parallel Displacements -- 6 Methods of Parallel Planes (PARP) -- 7 Modifications of Parallel Displacements Algorithms -- 8 CGS-Algorithms for Nonquadratic Functions -- 9 CGS-CG-Routines for Nonquadratic Functions -- 10 Gauss-Seidel CGS-Routines -- 11 The Case of Nonnegative Components -- 12 General Linear Inequality Constraints -- IV Conjugate Gradient Algorithms -- 1 Introduction -- 2 Conjugate Gradient Algorithms -- 3 The Normalized CG-Algorithm -- 4 Termination -- 5 Clustered Eigenvalues -- 6 Nonnegative Hessians -- 7 A Planar CG-Algorithm -- 8 Justification of the Planar CG-Algorithm -- 9 Modifications of the CG-Algorithm -- 10 Two Examples -- 11 Connections between Generalized CG-Algorithms and Stadard CG- and CD-Algorithm -- 12 Least Square Solutions -- 13 Variable Metric Algorithms -- 14 A Planar CG-Algorithm for Nonquadratic Functions -- References