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Jahn J. — Introduction to the Theory of Nonlinear Optimization
Jahn J. — Introduction to the Theory of Nonlinear Optimization

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Название: Introduction to the Theory of Nonlinear Optimization

Автор: Jahn J.

Аннотация:

This book serves as an introductory text to optimization theory in normed spaces. Topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 257

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$AC^n[t_0, t_1]$      27
$T(S, \bar{x})$      82
$W^{n}_{1, \infty} [t_{0}, t_{1}]$      107
$\tilde{C}$-quasiconvex      127
Adjoint equation      138 149
Alternation theorem      180
antisymmetric      249 250
Approximation problem      20
Arrow — Hurwicz — Uzawa condition      123
Asymptotically stable      193
Banach space      243
Basic version of the Hahn — Banach theorem      245
Bernoulli matrix differential equation      216
Best approximation      20
Binary relation      249
C(M)      22 175
Characterization of a convex functional      12 41
Chebyshev approximation      22
Clarke, derivative      68
Clarke, differentiable      68
Clarke, tangent cone      83 104
Closed loop control      218
Completely positive matrices      201
Concave functional      12
Cone      79 250
Cone (S)      81
Conic optimization      187
Conic optimization problem      188
Constraint set      1
Contingent cone      82 96 102 103
Controllable      137 149
Convex, functional      11 92 94
Convex, mapping      159
Convex, set      11
Convex-like mapping      160
Copositive optimization problem      190
Copositive ordering cone      190
d.c. functional      58
Directional derivative      31 54
Directionally differentiable      31
Doubly nonnegative ordering cone      190
Dual, cone      251
Dual, problem      164
Duality gap      165
Duality theory      207
Eidelheit separation theorem      245
Epigraph      9 103
Euler — Lagrange equation      48
F. John conditions      120
Feedback control      217 218
Fejer theorem      198
Frechet, derivative      39
Frechet, differentiable      39
Frechet, property      59 63
Fundamental matrix      223
Gateaux, derivative      38
Gateaux, differentiable      38
Generalized, gradient      73
Generalized, Kolmogorov condition      57
Generalized, Lagrange multiplier rule      110 116
Generalized, Slater condition      165 172 208
Generated cone      81 103
Hahn — Banach theorem      245 247
Hamilton function      149
Hautus condition      237
James theorem      243
John von Neumann saddle point theorem      169
K(T)      222
K-copositive optimization problem      190
K-copositive ordering cone      189
Kalman condition      149 237
Karush — Kuhn — Tucker conditions      120
Kurcyusz — Robinson — Zowe regularity assumption      115 118
Lagrange functional      115 168
Lipschitz, constant      59
Lipschitz, continuous      59
Local minimal point      18
Local Pontryagin maximum Local principle      138 149
Lowner ordering cone      189 197
Lowner partial ordering      189
Lyapunov function      194
Lyusternik theorem      96
Minimal point      1 7
Necessary optimality condition      36 43 47 53 55 56 66 74 89 90 95 108 111 137 230
Nonnegative ordering cone      190
normal      233
Objective functional      1
Open loop control      219
Optimal control problem      26 137 213 221
Optimality conditions      202
Optimization problem      7 106 162 172
Ordering cone      251
Partial ordering      249
Partially ordered linear space      249
Pointed cone      79 250
Pontryagin maximum principle      137
Positive cone      251
Positive homogenity      34
Primal problem      162 172 175
Problem of Chebyshev approximation      22
Problem of linear Chebyshev approximation      175 180
Proximinal      20
Pseudoconvex      91 94
Quasiconvex      14 93 94
Quasidifferentiable      57 63
Quasidifferential      57
Quasilinear      133
R(T)      223
Reachable set      223
Redundant constraint      124
Reflexive      243
Regularity assumption      114 118 123
Representation theorem for positive linear forms      178
Riccati matrix differential equation      219
Saddle point      168 169 170 172
Schur complement      191
Semi-infinite optimization problem      176 177
Semidefinite optimization problem      189
Separation theorem      246 248
Sequential Bouligand tangent cone      82
Set of attainability      222
Sgn(y)      228
Slater condition      123
Stabilizable      194
Starshaped set      35
Strong bang-bang principle      230 233
Strong duality theorem      165 208
Structural optimization      195
Subadditivity      34
Subdifferential      49 51 57
Subdifferential of the norm      50
Subgradient      49
Sublinear functional      34 103
Sufficient optimality condition      36 53 55 56 89 95 128 131 152
Superdifferential      57
Tangent vector      82
Transversality condition      138
U(T)      222
Uniform approximation      22
Weak, bang-bang principle      230
Weak, duality theorem      164 208
Weak, limit      241
Weakly convergent      241
Weakly lower semicontinuous      8
Weakly sequentially closed      242
Weakly sequentially compact      242
Y(t)      223
“Active” inequality constraints      121 124 133
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