Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
F.Giannessi, F.Giannessi - Constrained Optimization and Image Space Analysis
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Название: Constrained Optimization and Image Space Analysis
Авторы: F.Giannessi, F.Giannessi
Аннотация: Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers. Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.
It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2005
Количество страниц: 395
Добавлена в каталог: 10.05.2008
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Предметный указатель
Admissible cone 67
Affine(ly), function 95
Affine(ly), hull 52
Affine(ly), independent 52 275 328 329
Affine(ly), multifunction 286
Affine(ly), set 52
Alexandroff A.D. 226
Alternative, strong 308
Alternative, weak 308
Altitude of a simplex 10 37
Analytical complexity 129
Antitone functions 100
Archimedes 125
Astrodynamics 23 27
Bad convex functions 131-132
Base of a simplex 37
Bellman R. 237
Bellman Recurrence Equation 237
Bernoulli Jakob 36
Bernoulli Johann 36
Bilateral constraint(s) 1 3 4
Bouligand's contingent 126
Brachistochrone problem 36
Caratheodory theorem 50 328
Cauchy A.L. 226 228
Cavalieri B. F. 37
Centre of a set 127 128
Clarke derivative 153 156 157
Coerciveness 19 136 167 246
Combinatorial optimization 4 39 294
Comer point 57
Complementarity condition 316-317 322 330
Complementarity problem(s) 15 18 22 42
Complementarity systems 16 25 41 353
Complementarity vector system 17
Complex H-function 124
Complex minimum 8
Complex minimum point 8
Complex polar 77
Concave, set 47
Concave, strictly 48
Concavelike function 124 238 262 264
Cone(s) 58
Cone(s), acute 58
Cone(s), admissible 67 235
Cone(s), apex of 59
Cone(s), closed 4
Cone(s), convex 4
Cone(s), derived 235
Cone(s), differential 235
Cone(s), generated 61
Cone(s), hypertangent 68
Cone(s), interior 68
Cone(s), normal 68 114
Cone(s), pointed 4 58 86
Cone(s), polyhedral 61
Cone(s), properly pointed 58 59 90 126
Cone(s), reachable 67 235
Cone(s), right circular 6
Cone(s), solid 58 86
Cone(s), spanned 61
Cone(s), tangent 63 126 235
Conic extension 169 231 245 290
Conjugate function 116 117
Constrained problem(s) 2 4
Constraint(s), bilateral 1 3 4
Constraint(s), equilibrium 18
Constraint(s), unilateral 1 3 4
Contingent 126
Continuous Optimization 40 345
Convex, bad functions 131-132
Convex, body 47
Convex, closure 55
Convex, combination 48
Convex, cone 58
Convex, function 95
Convex, geodesic hull 293
Convex, hull 48 293
Convex, multifunction 286
Convex, proper combination 48
Convex, set 47
Convex, strictly (set) 47
Courant R. 308
Cutting halfspace 369
Cycloid 36
deFermat P. 10 37
Derivative(s), Clarke 153
Derivative(s), Dini directional 153
Derivative(s), directional 143 330
Derivative(s), Frechet 191
Derivative(s), G- 143
Derivative(s), G-semi 150 225
Derivative(s), Gateaux 191
Derivative(s), partial G- 143
Descent method 36
Dido's problem 10 35
Differentiable functions 110
Differentiable functions, 144 152
Differentiable functions, 144
Differentiable functions, semi- 150 158
Differential, G- 148
Differential, G-sub 147
Differential, G-super 148
Differential, sub- 110
Dimension of a face 73
Dini, directional derivatives 150
Dini, Theorem 321
Discrete optimization 4 294 301 345
Duality 308
Equilibrium, constraints 18
Equilibrium, flows 28 29
Erdos P. 10 37
Erdos problem 10 37
Euler L. 10 36 127 307 363
Euler, equation 307 332
Excess function 98
Extreme point 48
Face of a set 73 127
Face of a set, dimension of 73
Face of a set, exposed 73
Face of a set, improper 73
Face of a set, minimal 73
Face of a set, proper 73
Fan 287
Farkas J. 78 251 270 284 294 302
Fasbender E. 37
Feasible region 1 2
Feasible solution 2
Fenchel inequality 116
Fermat - Torricelli problem 10 37
Fixed-charge 40
Flight mechanics 23 26
Function(s), -differentiable 144
Function(s), (non)decreasing 100
Function(s), (non)increasing 100
Function(s), affine 95
Function(s), antitone 100
Function(s), bad convex 131-132
Function(s), C-differentiable 144 152
Function(s), coercive 19 136
Function(s), complex H- 124
Function(s), concave 95
Function(s), concavelike 124 238 262
Function(s), conjugate 116 117
Function(s), convex 95
Function(s), convexlike 124
Function(s), differentiable 110
Function(s), directionally derivable 143
Function(s), excess 98
Function(s), G-derivable 143
Function(s), G-differentiable 143
Function(s), G-semidifferentiable 150
Function(s), gauge 115-116
Function(s), geodesic convex 124
Function(s), Green 25
Function(s), H- 124
Function(s), H-concavelike 124 262
Function(s), H-convex 124 136
Function(s), H-convexlike 124 136
Function(s), Hamiltonian 366
Function(s), indicator 114 115 117
Function(s), isotone 100
Function(s), Lagrangian 192-194 198 312 313 316 322 331 366
Function(s), likelihood 31
Function(s), max- 7 116
Function(s), Minkowski 115-116
Function(s), monotone 100
Function(s), multi- 15 180 354
Function(s), norm 114
Function(s), objective 2
Function(s), optimal value 167
Function(s), parabolic exponential 258 313
Function(s), Peano 122 136
Function(s), perturbation 167
Function(s), positively homogeneous 107 108 116 143 225
Function(s), pseudoantitone 122
Function(s), pseudoconcave 120
Function(s), pseudoconvex 120 135
Function(s), pseudoisotone 122
Function(s), quasiconcave 117-118
Function(s), quasiconvex 117-118 133
Function(s), selection 181 279 282 295
Function(s), semidifferentiable 150 158 224
Function(s), separation 252 254 258 259 290
Function(s), stricly quasiconcave 117-118
Function(s), strictly antitone 100
Function(s), strictly concave 95
Function(s), strictly convex 95
Function(s), strictly isotone 100
Function(s), strictly pseudoconcave 120
Function(s), strictly pseudoconvex 120
Function(s), strictly quasiconvex 117-118
Function(s), strong separation 255 289
Function(s), strongly convex 114
Function(s), subadditive 107
Function(s), subdifferentiable 110
Function(s), sublinear 107 143
Function(s), sum-decomposable 293
Function(s), superlinear 107
Function(s), support 76 116 117
Function(s), weak separation 252 254 258 282 290 299 310 312
Galilei G. 36
Gauge function 115-116
Generalized selective functions 279 282 295
Generalized systems 15 18
Generalized systems, parametric 18
Geodesic, convex functions 124
Geodesic, convex hull 293
Geodesic, set 38
Geodesic-type problem 3 4
Global minimum point 1
Global vector minimum point 5
Gozzi L. 39
Gradient, G-sub 148
Gradient, G-super 148
Gradient, semi- 224
Gradient, sub- 110
Graves L.M . 15
H-convex function 124
H-function 124
Hahn - Banach theorem 70-71 251
Hamiltonian function 366
Hartman - Stampacchia Theorem 19
Helly theorem 51 278
Hestenes M .R. 235
Hilder condition 347
Holomorphic field 135
Homogenization Lemma 172 195 197 235 328
Homogenization of the image 169 239 241 245 321-322 327-328
Hypertangent cone 68
Image 165 180 285
Image, conic extension of 169
Image, homogenization of 169
Image, perturbed problem 165
Image, selected 187 285 364
Image, space 165 180
Incidence-matrix 29
Indicator function 114 115
Inequality, Fenchel 116
Inequality, isoperimetrical 48 335 337 339 366
Inequality, Jensen 98
Inequality, Jung 53
Inequality, Minty Vector Variational 16
Inequality, Stampacchia Vector Variational 16
Inequality, Variational 15 16 42 242 353 372
Inequality, Vector Variational 16
Interior, cone 68
Interior, quasi relative 61
Isodiametrical problems 38
Isoperimetric(al) inequality 48 335 337 339 366
Isoperimetric(al) problems 10 36 38 334
Isoperimetric(al)-type problems 2 4
Isoproblems 38
Isotone, function 100
Isotone, gradient 114
Jensen inequality 98
John F. 321
Jordan - Brower Theorem 294
Jung Inequality 53
Lagrange G.L. 10 36 307 308 316 320 321-322 329 363
Lagrange G.L., auxiliary function 366
Lagrange G.L., Method of Multipliers 307 308 320 321-322 329
Lagrange G.L., necessary conditions 308 320 331-332
Lagrange G.L., principle 363
Lavel set 252
Lemma, Farkas 251 270 284 294
Lemma, Homogenization 172 195 197 235 328
Lemma, Linearization 172
Lemma, Minty 16
Lemma, Neyman - Pearson 32
Likelihood function 31
Linearization Lemma 172
Ljusternik Theorem 321
Local minimum point 1
Lower, semistationary point 1
Maier G. 19 22
Malfatti G. 38 39
Malfatti problem 38-39
Map(ping)s see 'Functions'
Matrix, incidence 29
Max-function 7 116
Maximum principle 364
Maximum Principle, Bellman 237
Maximum Principle, Dubovitskii - Milyutin 130 240
Maxmin problems 7
Mayer's problem 14
Mean arithmetic 336
Mean geometric 336
Mean harmonic 336
Mengoli P. 226
Mersenne M . 10
Method(s), decomposition 244
Method(s), descent 36
Miele A. 26 28
Minimax problems 7 13 38
Minimum point 1
Minimum point, complex 8
Minimum point, global 1
Minimum point, global vector 5
Minimum point, isolated 1
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