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F.Giannessi, F.Giannessi — Constrained Optimization and Image Space Analysis
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 395

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\mathcal{C}-$      144 152
Differentiable functions, $\mathcal{L}-$      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), $\mathcal{L}$-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
1 2
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