Craven B.D. — Mathematical Programming and Control Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Craven B.D. — Mathematical Programming and Control Theory

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Название: Mathematical Programming and Control Theory

Автор: Craven B.D.

Аннотация:

This book presents a unified theory of nonlinear mathematical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e.g. a continuous curve (i.e. infinitely many variables). The underlying ideas of vector space, convex cone, and separating hyperplane are the same, whether the dimension is finite or infinite; and infinite dimension makes very little difference to the proofs. Duality theory - the various nonlinear generalizations of the well-known duality theorem of linear programming - is found relevant also to optimal control, and thePontryagin theory for optimal control also illuminates finite dimensional problems. The theory is simplified, and its applicability extended, by using the geometric concept of convex cones, in place of coordinate inequalities.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 173

Добавлена в каталог: 16.05.2011

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Предметный указатель

Adjoint differential equation      80 87
Affine hull      20
Algorithms      119
Algorithms, Beale      139
Algorithms, conjugate gradient      127
Algorithms, Davidon — Fletcher — Powell      130
Algorithms, decomposition      141
Algorithms, Dinkelbach      108
Algorithms, false position      124
Algorithms, feasible directions      134
Algorithms, Fletcher — Reeves      128
Algorithms, fractional programming      106
Algorithms, Frank and Wolfe      107
Algorithms, Lagrangean      136
Algorithms, Newton      123 126
Algorithms, projection      134
Algorithms, quadratic programming      66 139
Algorithms, sequential unconstrained minimization      131
Algorithms, steepest descent      125
Algorithms, unconstrained minimization      125
Algorithms, Wolfe      66
Alternative Theorems      31 32 33
Bang-bang control      69 77 85
Barrier function      132
Basic alternative theorem      31
Beale      139 145
Bennett      142 144 145
Complementary slackness      59
Complex programming      109
Cone inclusion theorem      24
Conjugate gradients      127
Constraint qualifications      51 56 58 61 62 63
Control problems      5 14 66 67 76 79 81 82 87 138
Control problems-abstract formulation      14 79
Convergence rate      122 123 124 126 128 130 133
Converse duality      73
Convex cones      22
Convex cones with empty interior      154
Convex duality      57
Convex functions      27 28 31 32 49 51 52 55 57 70 78 102 103 112 136 158
Convex geometry      19
Convex minimization problems      51 69 81 112 136
Critical points      27
Cutting stock problem      91
Dantzig      40 142 145
Davidon — Fletcher — Powell method      130
Decentralized resource allocation      4 49 57
Decomposition      141
Derivatives, Frechet      13
Derivatives, Gateaux      14
Derivatives, Hadamard      19 156
Differentiable functions and zeros      152
Differentiable Lagrangean theory      58 65
Differentiable minimization problems      58 69
Dinkelbach method      108 117
Direct sum      12
Duality      38 51 69 96 98 104 106 114
False position      124
Farkas Theorem      24 32 33 151
Fletcher — Reeves method      128
Fractional programming      91 93 99 106
Fractional programming, algorithms      106
Fractional programming, applications      91
Fractional programming, duality      96 98 104 106
Frank and Wolfe method      107 117
Fritz John theorem      59 80 113 115
Halfspace      20 25

Hamiltonian      79 82
Homogeneous duality      104
Hyperplane      20
Implicit function theorem      8 34 147
Interior of cone      154
Interpolable      82 83
Karlin 's constraint qualification      51 52
Kuhn — Tucker constraint qualification      61 67
Kuhn — Tucker theorem      60 61 63 65 76 104 137
Lagrange multipliers      7 38 52 58 137
Lagrangean      7 16 38 49 55 64 137
Lagrangean necessary, conditions      7 16 38 59 64 65 76 80 137
Lagrangean sufficient, conditions      64 65 77 81
Linear fractional programming      93
Linear programming      36 38 40 47 94 98 141
Linear programming duality      38 57 96 98
Linear systems      36
Linearization      33 34
Local minimum      27 28 119
Local solvability      33 34 59 60 78 81 87 147
Lootsma      133 145
Luenberger      136 145
Measurable functions      155
Motzkin alternative theorem      32 33 59 110
Nondifferentiable problems      51
Nonlinear fractional programming      99
Optimal control      6 14 66 76 79 82 87 138
Parametric programming      45
Penalty functions      131
Perturbations      51
Pietrzykowski      134 146
Pointwise theorems      82
Polyhedral cones      26 33 61
Pontryagin theory      77 80 81 83 85 86 87 89 123 139
Portfolio selection      92
Production allocation      3
q-equivalent      94 97 98 100
Quadratic programming      50 65 67 139
Quasimin      78
Regular      60 61
Representation of dual spaces      11 17 86
Robinson      150 151
Rockafellar      138 146
Rocket      5
Saddlepoint theorem      52
Separable programming      46
Separation theorem      23 32 54 55 56
Sequential unconstrained minimization      131
Shadow costs      40 57
Shipping scheduling      92
Simplex method      40 45
Slater's constraint qualification      51 56 58
Stable      53 54 56
Steepest descent      125
Stochastic programming      93
Subgradient      53 54
symbols      9
Symmetric duality      114
TEO      139 146
Transportation network      2
Transversality      17 59 68
Variable endpoint problems      87
Weak duality      39 55 70 96 105
Wolfe      66 70 75 107 117 142 145
Wolfe's duality      70 72
Zeros of differentiable functions      152
Zoutendijk      134 146

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