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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
Minimum point, local 1
Minimum point, strict 1
Minimum point, strong 1
Minimum, complex 8
Minimum, partial 7
Minimum, quasi- 6
Minimum, vector 5
Minkowski function 115—116
Minty G.J. 16
Minty G.J., Lemma 16
Minty G.J., Variational Inequality 16
Minty G.J., Vector Variational Inequality 16
Monotone maps, (non)decreasing 100
Monotone maps, (non)increasing 100
Multifunctions 15 180 279 283 295 354
Multifunctions, affine 286
Multifunctions, C- 286
Multifunctions, C-concave 286
Multifunctions, C-convex 286
Multifunctions, cone 285
Multifunctions, convex 286
Multifunctions, homogeneous 286
Multifunctions, linear 286
Multifunctions, preaffine 286
Multifunctions, selection of 279
Multifunctions, theorems of the alternative 279
Multiplier(s) 307 308
Multiplier(s), selection 280 282 364
Network flows 28
Newton I. 36
Neyman — Pearson lemma 32
Norm function 114
Normal cone 68 114
Objective function 2
Obstacle problem 12 22—23
Optimal value function 167
Ordering partial 4
Orthogonality condition 316
Parabolic-exponential functions 258 313
Parametric generalized system 18
Pareto problems 5
Partial maximum 7
Partial order(ing) 4 8
Peano function 122 136
Penalization 346 371
Penalization, exterior 308
Penalization, interior 308
Perturbation function 167
Point, complex minimum 8
Point, corner 57
Point, extreme 48
Point, generalized Torricelli 128
Point, global minimum 1
Point, isolated minimum 1
Point, local minimum 1
Point, lower semistationary 1 190
Point, minimum 1
Point, quasi-minimum 6
Point, saddle 13
Point, stationary 2 191
Point, strict minimum 1
Point, strong minimum 1
Point, Torricelli 10 128
Point, upper semistationary 1 191
Pointed cone 58 126
polar 58 75 77
Polar complex 77
Polar cone 58 77
Polar negative 77
Polar positive 77
Polar vector 17 78
Polyhedron 57 73
Polyhedron, face of 73
Polytope 52 57 73 86
Polytope, face of 73
Pontryagin maximum principle 363—364
Positively homogeneous functions 107 108 116 143 225
Prager W. 24 294
Principle, (of) reciprocity 339—340
Principle, Lagrangian 363
Principle, Pontryagin 363—364
Problem(s) with equilibrium constraints 18
Problem(s), allocation 12
Problem(s), brachistochrone 36
Problem(s), Combinatorial Optimization 4 345
Problem(s), complementarity 15 18 22
Problem(s), constrained 2
Problem(s), Discrete Optimization 4 345
Problem(s), Erdos 10 37
Problem(s), Fermat — Torricelli 10 37
Problem(s), fixed-charge 40
Problem(s), geodesic-type 3 4
Problem(s), image 165
Problem(s), isodiametrical 38
Problem(s), isoperimetrical (type) 2 4 10 35 334
Problem(s), Malfatti 38
Problem(s), maxmin 7
Problem(s), Mayer’s 14
Problem(s), obstacle 12 22—23
Problem(s), perturbated image 165
Problem(s), quasi-minimum 6
Problem(s), reciprocal 9 339
Problem(s), Signorini 42
Problem(s), unconstrained 2
Problem(s), Vector (optimization) 5 32 362
Pseucoconvex functions 120 122 135
Pseudo-manifold 294
Pseudoantitone map 122
Pseudoconcave functions 120
Pseudoisotone map 122
Pyramid 61
Quasi concave functions 117—118
Quasi convex functions 117—118 133
Quasi relative interior 61
Quasi-minimum point 6
Quasi-minimum problem 6
Quasi-variational inequality 16 41
Radon theorem 51
Reachable cone 67
Reciprocal problem 9 339—340
Relaxation(s) 17 224 346
Riemann G.F. 226
Saddle point 13 308 313—315
Saddle value 13 314
Selection of multifunctions 279
Selection, function 181 279 282 295
Selection, multiplier 181 187 280 364
Semidifferentiability 143
Semidifferentiable functions 150 158
Semidifferentiable functions, lower G- 150 224
Semidifferentiable functions, upper G- 150
Semistationary point 1 190
Separable sets 80
Separating hyperplane 80 322
Separation 80 275
Separation, among several sets 129 130
Separation, disjunctive 80
Separation, functions 252 255 258 259 289 299 310
Separation, nonlinear 252
Separation, proper 80
Separation, stable 81
Separation, strict 80
Separation, strong 81 308
Separation, theorems 251 275
Separation, weak 308 309 320
Set, centre of 127
Set, face of 73
Set, polar of 75 86 87
Set, polyhedral 57
Set, separable 80
Set, star of 54
Set, star-shaped 54
Signorini problem 42
simplex 10—11 52 57 294
Simplex, altitude of 10 37
Simplex, base of 37
Simplex, face(t) of 53
Simplex, m- 52
Simplex, sub- 52
Simpson T. 37
Stampacchia G. 15 16 19 42
Stampacchia, Variational Inequality 16
Stampacchia, Vector Variational Inequality 16
Stationary point 2 191
Steiner J. 37
Strict minimum point 1
Strong minimum point 1
Strong separation functions 255 289
Subadditive functions 107
Subdifferential 110
Subdifferential, G- 147
Subgradient 110
Subgradient, G- 148
Sublinear functions 107 143
Superlinear functions 107
Support(ing) 70
Support(ing), function 76 116
Support(ing), halfspace 70
Support(ing), hyperplane 70 115 117
Support(ing), lower 225
Support(ing), point 70
Support(ing), proper 70
Support(ing), strict 70
System(s), complementarity 16 25 42 353
System(s), generalized 15
System(s), of intersection type 289
System(s), parametric generalized 18
System(s), Vector complementarity 17
Tangent cone 63
Theorem(s), Caratheodory 50 328
Theorem(s), Dini 321
Theorem(s), Ekeland 167 229
Theorem(s), excess function 98
Theorem(s), Hahn — Banach 70—71
Theorem(s), Hartmann — Stampacchia 19
Theorem(s), Helly 51 251 278
Theorem(s), Jordan — Brower 294
Theorem(s), Ljusternik 321
Theorem(s), Rademacher 226
Theorem(s), Radon 51
Theorem(s), Rouche — Capelli 271
Theorem(s), separation 251 275
Theorem(s), Weierstrass 6
Theorems of the Alternative 251 260 266 289 291
Theorems of the Alternative, (for) multifunctions 279
Theorems of the Alternative, (in a) Complex Space 298
Theorems of the Alternative, Duffin 251 272
Theorems of the Alternative, Fan — Glicksberg — Hoffman 267
Theorems of the Alternative, Farkas 251 270 284
Theorems of the Alternative, Gale 271
Theorems of the Alternative, Gordan 251 267 268 294
Theorems of the Alternative, integer Farkas 302
Theorems of the Alternative, Jordan — Brower 294
Theorems of the Alternative, Mangasarian 273
Theorems of the Alternative, Motzkin 251 268
Theorems of the Alternative, Slater 251 269
Theorems of the Alternative, Stiemke 251 270
Theorems of the Alternative, Strong 290—291
Theorems of the Alternative, Tucker 269
Theorems of the Alternative, weak 290—291
Time-lag 41
Torricelli E. 10 37
Torricelli point 10 128
Unconstrained problem 2
Unilateral constraint(s) 1 3 4
Upper semistationary point 1 191
Variational inequalities 15 16 42 242 353 372
Variational Minty Inequality 16
Variational Minty Vector Inequality 16
Variational Quasi- 16 41
Variational Stampacchia Inequality 16
Variational Stampacchia Vector Inequality 16
Variational Vector Inequality 16
Vector, Complementarity System 17
Vector, global minimum point 5
Vector, Minimum 5
Vector, Optimization 5 32 362
Vector, Pareto 5
Vector, polar 17 78
Vector, problems 32
Vector, Variational Inequality 16
Vector, weak Pareto 5
Vertex 57
Viviani V. 37
Volpato M. 237
Volume of a simplex 11 37
von Neumann J. 38 133
Wardrop J.C. 40
Weak Pareto problems 5
Weak separation functions 252 254 258 282 289 299 310
Weber A. 37
Weierstrass, excess function 98
Weierstrass, theorem 6
Zenodorus 3
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