Fletcher R. — Practical methods of optimization. Volume 1: unconstrained optimization :: Электронная библиотека попечительского совета мехмата МГУ

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Fletcher R. — Practical methods of optimization. Volume 1: unconstrained optimization

Fletcher R. — Practical methods of optimization. Volume 1: unconstrained optimization

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Название: Practical methods of optimization. Volume 1: unconstrained optimization

Автор: Fletcher R.

Аннотация:

Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 120

Добавлена в каталог: 19.07.2005

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Предметный указатель

Acceptable $\alpha$ -value      20 26
Alternating variables method      15 70
Angle test      21 23
Autonomous system      106
BFGS formula      44 55
BFGS method      61
Bisection      13 26
Boxstep method      81
Bracket      26 29 87
Brown — Brent method      109
Broyden family      44 48 61 62
Broyden formula      109 112
Broyden method      50 52
Chebyquad function      54 66 87 89 95
Chebyshev semi-iteration      103
Choleski factorization      13 43 47
Complementary formula      44
Condition number      23 95 96
Conditioning      47 59 85
Conjugate descent formula      66
Conjugate direction method      16 24
Conjugate directions      24 43 50 58 63 64 70
Conjugate gradient method      51 63 68
Conjugate gradients      43
Conjugate vectors      24 32
Constraints      3
Continuation method      103
contour      5
Contraction mapping      103
Convergence      35 53 99
Convergence test      19
Convergence, global      16 21 23 43 44 53 69 78
Convergence, linear      17 31 102 110
Convergence, quadratic      17 103
Convergence, rate of      17 53
Convergence, second order      35 69 80 99
Convergence, superlinear      17 43 53
Convex class      54
Convex function      43 53
Curvature      6 11
Data fitting      91 110
Davidenko path      103 111
Davidon family of formulae      58
Degenerate value      50 62
Descent condition      64
Descent method      18 20 105
Descent property      20 22 23 66 95
DFP formula      42 57
DFP method      42 53 61
Difference approximation      20 45 74 81 82 106
Direction      5
Direction set method      70
Dixon's theorem      52 55
Dog-leg trajectory      81 88 90 108
DSC method      16
Dual formula      44 59
Euclidean norm      59 75
Exact line search      17 24 28 43 50 52 53 63
Experimentation      17 54
Extrapolation, cubic      27 55
Extrapolation, quadratic      27 55
Fibonnaci section search      29
Finite difference approximation      20 45 74 81 82 106
Finite difference Newton method      38
First order necessary conditions      38 78 82
Fixed point      101
Fletcher switching formula      54 57
Fletcher — Reeves method      51 63 75
Freudenstein and Roth equations      99 104
Gauss — Newton method      93 106 110
Gauss — Newton method with line search      94
Gauss — Seidel method      102
Generalized least squares method      93
Gershgorin discs      87
Global convergence      1 6 21 23 43 44 53 69 78
Global minimization      100 106
Global minimum      10 30 89
Global solution      83
Golden section search      29 31
Goldstein conditions      20
GOT method      82
Gradient vector      6
Hereditary property      41 50 107
Hessian matrix      6
Hooke and Jeeves method      16
Hoshino formula      54 57
Huang family      49 59
Hypercube method      81
Hypercube trajectory      89
Ill-conditioning      47 85 87
Incomplete Choleski factorization      69
Indefinite matrix      13
Independent vectors      32 51 52
Inexact line search      18 44 53 55
Interpolation      26
Interpolation, cubic      28
Interpolation, quadratic      26
Invariance      38 44 45 59
Jacobi method      102
Jacobian matrix      92
Lagrange multiplier      62 82
Large problems      68
LDLT factorization      13 33 45
Least squares      91 93
Level set      79
Levenberg — Marquardt method      37 82 96 100
Levenberg — Marquardt trajectory      84 86 89
Line      4
Line search      42 55 78 99 110
Line search algorithm      17 25
Line search, exact      17 24 28 43 50 52 53 63
Line search, inexact      18 44 53 55
Line search, partial      18
Linear approximation      93 98 107
Linear convergence      17 31 102 110
Linear function      7 111
Linear transformation      45 59
Linear variables      98

LLT factorization      87 96 111
Local minimum      10 30 89
LU factorization      98 109
Mathematical model      3
Matrix      4
Maximization      10
Maximum likelihood solution      93
Metric      45 48 81
Minimal correction formula      59 62
Minimizer      10
Minimizer, isolated local      11
Modified Newton method      47 87
Necessary conditions      11
Necessary conditions, first order      38 78 82
Necessary conditions, second order      38 78 83
Negative curvature direction      37 61 76
Negative definite matrix      13
Newton — Raphson method      98 106 110
Newton's method      33 47 48 60 77 93
Newton's method with line search      35 47
Newton-like method      46 88
No-derivative method      70 82 106
No-derivative problem      45
Non-differentiable optimization      92
Non-linear equations      91
Non-linear least squares      91 106
Non-smooth minimum      10
Norm      7 48 81 92 100
Norm, Euclidean      59 75
Norm, weighted      75
Normal equations      93
o(*) notation      12
Objective function      2
Optimal conditioning      59
Orthogonal Factorization      97 98 108 109.111
Orthogonal gradients      51 64
Orthogonal transformation      62 74
Over-determined equations      91
Parallel subspace property      70
Partial line search      18
Point      4
Polak — Ribiere formula      66 69
Positive definite matrix      11 12 23 33 38 43 83
Positive semi-definite matrix      11 83 95
Powell dog-leg trajectory      81 88 90 108
Powell's method      72
Preconditioning      69
Programming      1
Projection formula      58 66
Quadratic convergence      17 103.
Quadratic extrapolation      27 55
Quadratic function      7 23 50 63 70
Quadratic model      23 33
Quadratic program      81
Quadratic termination      24 41 42 50 53 58
Quasi-Newton condition      39 43 44 59
Quasi-Newton method      38 47 65 68 74 81
Random search      14
Rank one formula      41 107
Rank one matrix      39 47 107 112
Rank one method      41
Rank one modification      45
Rank two formula      4 2
Rank two matrix      42 48
Rate of convergence      53
Residuals      91
Restricted step method      37 77 82
Rosenbrock's function      5 29 54 66 87 95
Round-off errors      45 85 96
Saddle point      36
Scalar product      4
Scaling      47 59 81 87
Secant method      107 111
Second order conditions      37
Second order convergence      35 69 80 99.
Second order necessary conditions      38 78 83
Second order sufficient conditions      80 83
Sectioning      14 26 87
Self-dual formula      44 62
Self-scaling method      59
Sherman — Morrison formula      61
Simplex method      14
Singular value decomposition      97
slope      6 11
Smith's method      71 76
SOR method      103
Sparse matrix      59 107 109
Spectral radius      103
Standard deviation      110
Stationary point      13 36 37 76
Statistics      93
Steepest descent direction      36 48 88
Steepest descent method      18 30 47 62 63
subspace      24
Successive substitution method      101 111
Sufficient conditions      11
Sufficient conditions, second order      80 83
Sum of squares      91
Sum of squares problem      110
Superlinear convergence      17 43 53
Switching formula      54 57
Symmetric Huang family      49 59
Taylor series      8 33 77
Termination      88 107
Termination test      19
Termination, quadratic      24 41 42 50 53 58
Test problems      1 7 54
Triangular factors      13
Trigonometric function      55 66 87 95
Trust region      77
Updating formula      39 107 109
User subroutine      5 5
Variable metric method      39 48
Variance      93
Variance-covariance matrix      9*3 110
Vector      4
Weighted norm      75
Well-determined equations      91 98
Wild points      92

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