Magaril-Il'yaev G.G., Tikhomirov V.M. - Convex Analysis: Theory and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Magaril-Il'yaev G.G., Tikhomirov V.M. - Convex Analysis: Theory and Applications

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Название: Convex Analysis: Theory and Applications

Авторы: Magaril-Il'yaev G.G., Tikhomirov V.M.

Аннотация:

This graduate textbook illustrates the fundamentals of convex analysis in a finite dimensional setting, examines the properties of convex sets and convex functions, and provides applications of convexity theory to the duality of convex calculus and to extremal problems of approximation and recovery. Originally published in Russian as Vypuklyi analiz teoriia i prilozheniia in 2000

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 183

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Accumulation point      28
Admissible point (in an extremal problem)      70
Affine combination (of vectors)      31
Affine hull (of a set)      31
Affine independent points      31
Affine manifold      13 26 31
Affine subspace      13 26 31 80
Algebraic sum      30
Analog of Fermat's theorem      49
Annihilator      42 81
Banach - Alaoglu theorem      153
Barycentric coordinates      32
Basis      25
Bernstein's inequality      138
Biannihilator      42 81
Biconjugate cone      81
Bipolar      81
Blaschke's compactness theorem      68
Brunn - Minkowski inequality      67
Brunn - Minkowski symmetrization      67
Caratheodory's theorem      8 62
Cauchy theorem on rigidity      58
Cauchy - Steiner lemma      60
Cauchy's formula      65
Clean-up theorem      156
Clean-up theorem for cones      62
Closed set      4 27
Closure      28
Compact set      28
Complementary slackness condition      71
Cone      13 30
Conic combination      31
Conic hull (of a set)      31
Conjugate cone      42 81
Conjugate function      15 39
Conjugation operator      39
Conjugation operator for cones      42
Constraint      70
Continuous function      28
Convex analysis      1
Convex closure      7
Convex combination      31
Convex cone      13 31 80
Convex curve      1
Convex function      1 34
Convex homogeneous function      13
Convex hull      7
Convex hull of a set      31
Convex hull of a union (of convex sets)      53
Convex hull of minimum (of convex functions)      54
Convex polyhedron      88
Convex Problem      19 69
Convex programming problem      19 70
Convex set      1 30 31 80
Convex surface      1
Convolution (of convex functions)      54
Directional derivative      36
Distance between vectors      27
Dual problem      21
Dual problem (to an extremal problem)      73
Dual space      26
Dubovitskii - Milyutin formula      17
Dubovitskii - Milyutin theorem      52
Epigraph      1 34
Euclidean norm      27
Extremal subset      154
Extreme point      154
Farkas Theorem      90
Fenchel - Moreau theorem      11 16 44
Fermat - Torricelli - Steiner problem      96
Finitely generated cone      88
First separability theorem      38
Fredholm theorem      92
Fuller, A.T.      111
Gabushin, V.N.      111
Gale theorem      90
Generalized Gabushin's inequality      110
Generalized Hoelder's inequality      93
Goddard problem      97
Gruenbaum - Hammer theorem      68
Hahn - Banach - Kantorovich theorem      161
Half-interval      29
Half-space      37
Helly's theorem      9 63
Hoelder's inequality      93
Homogeneous function      13
Hyperplane      26 37
Image of a function under a mapping      35 54
Image of a set under a mapping      30 53
Indicator function      42
Indicator function of a convex set      34
Indicator operator      42
Interior of a set      27
Interior point of a set      27
Intersection      30
Intersection of convex sets      53
interval      29
Inverse image of a function under a mapping      35 54
Inverse image of a set under a mapping      30 53
Jensen inequality      34

Karush - Kuhn - Tucker theorem      20 70
Kelley's sum of convex functions      54
Kelley's sum of convex sets      53
Kolmogorov-type inequalities      99
Ky Fan theorem      90
Lagrange function      70 163
Lagrange multipliers      70 163
Lagrange principle      20
Landau - Arestov theorem      118
Least possible constant      100
Legendre transform      39
Legendre - Young - Fenchel transformation      15
Lemma on nontriviality of the annihilator      168
Lemma on the annihilator of the kernel of a regular operator      165
Levin's theorem      52 156
Line segment      27 29
Linear combination (of vectors)      30
Linear programming problem      74
Linear span (of a set)      31
Locally convex space      13
Lyapunov, A.A., theorem      155 169
Lyusternik theorem      165
Magaril-Il'yaev theorem      116 118
Magaril-Il'yaev, G.G.      111
Masur theorem      160
Maximum (of convex functions)      35 54
Method of central sections      75
Method of circumscribed ellipsoids      76
Michael's selection theorem      161
Minkowski - M. Krein - D. Milman theorem      7 154
Minkowski's function      36 43
Minkowski's operator      43
Minkowski's theorem      6 64 90
Monge - Kantorovich problem      158
Moreau - Rockafellar formula      17
Moreau - Rockafellar theorem      51
Neighborhood      27
Nonatomic measure      155
Open ball      27
Open set      4 27
Perturbation of problem      21 72
polar      41 81
Polyhedral cone      88
Problem without constraints      20 49 70
Proper function      34
Rademacher theorem      160
Radon theorem      9 62
Ray      27
Relative interior (of a set)      32
Relatively interior point (of a set)      32
Riesz, F., theorem      92
Riesz, M., identity      138
S-function (of the family of problems)      72
Second conjugate      15 40
Second separability theorem      37
Second separation theorem      4 83
Separable sets      37
Separation theorems      16 37
Set of constraints      70
Sharp constant      100
simplex      31
Simplex method      77
Slater's condition      70
Solution (to an extremal problem)      70
Standard basis      25
Standard perturbation      73
Stationarity condition      101
Steiner - Minkowski formula      66
Straight line      27
Strictly differentiable mapping      164
Strictly separable sets      37
Subdifferential      17 40 48
Subdifferential form of the clean-up theorem      52
Subgradient      17 48
Sublinear function      13 35
subspace      13 26 30 80
Sum of convex functions      54
Sum of convex sets      53
Summation (of convex functions)      35
Support function      18 36 41
Support operator      41
Sz.-Nagy, B.      106 107
Sz.-Nagy, B. theorem      108
Tangent vector      164
Theorem on convex duality      43
Theorem on duality of sets      83
Theorem on existence and structure of subdifferential      50
Theorem on isoperimetric property of circle      94
Theorem on polyhedral sets      69
Theorem on strict separation      4
Theorem, Lagrange principle for smooth-convex problems      164
Theorem: the main formulas of convex calculus      55
Value (of an extremal problem)      70
Vertex      31
Weak topology      82
Weierstrass theorem      29
Weyl theorem      88
Young - Fenchel transform      39
Young's inequality      94
Zero-convex set      13 80

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