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F.Giannessi, F.Giannessi — Constrained Optimization and Image Space Analysis
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Название: Constrained Optimization and Image Space AnalysisАвторы: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2005Количество страниц: 395Добавлена в каталог: 10.05.2008Операции: Положить на полку |
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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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