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Zalinescu C. — Convex Analysis in General Vector Spaces
Zalinescu C. — Convex Analysis in General Vector Spaces

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Название: Convex Analysis in General Vector Spaces

Автор: Zalinescu C.

Аннотация:

The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 367

Добавлена в каталог: 19.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Best approximation      237
Bomology      190
Bomology, Frechet      190
Bomology, Gateaux      190
Bomology, Hadamard      190
Cone      1
Cone, dual      7
Cone, normal      87
Cone, recession      6
Cone, tangent (of Clarke)      169
Convolution      43
Directional derivative      56
Directional derivative, $\varepsilon-$      58
Directional derivative, Clarke — Rockafellar      171
Directional derivative, upper Dini      58
Domain of function      39
Domain of multifunction      12
Domain of operator      42
Duality mapping      230
Duality strong      107
Duality weak      107
Epigraph of function      39
Epigraph of function, strict      39
Epigraph of operator      42
Function, $\psi$-conditioned      196
Function, $\psi$-conditioned, with respect to      196
Function, $\rho$-convex      203
Function, $\sigma$-smooth      204
Function, $\sigma$-smooth, on a set      204
Function, B-differentiable      191
Function, bcs-complete      68
Function, coercive      100
Function, coercive, strongly      214
Function, concave (strictly)      40
Function, conjugate (Fenchel)      75
Function, convex      39
Function, convex, strictly      40
Function, convex, strongly      203
Function, cost      99
Function, cs-closed      68
Function, cs-complete      68
Function, cs-convex      67
Function, distance      237
Function, ideally convex      68
Function, indicator      41
Function, Lagrange      138
Function, lcs-closed      68
Function, li-convex      68
Function, Lipschitz      66
Function, Lipschitz, locally      66
Function, marginal      43
Function, objective      99
Function, performance      107
Function, perturbation      106
Function, proper      39
Function, Q-decreasing      42
Function, Q-increasing      42
Function, quasi-continuous      67
Function, quasi-convex      41
Function, recession      74
Function, S-smooth      191
Function, subdifferentiable      80
Function, sublinear      4
Function, support      79
Function, uniformly convex      203
Function, uniformly convex, at a point      201
Function, uniformly convex, on a set      203
Function, uniformly convex, on bounded Function, sets      221
Function, uniformly Frechet differentiable      207
Function, uniformly smooth on a set      207
Function, uniformly smooth on bounded sets      221
Function, value      107
Function, weight      227
Function, well-behaved (asymptotically)      259
Function, well-conditioned      197
Gage of conditioning      196
Gage of smoothness (midpoint)      205
Gage of uniform convexity      203
Gage of uniform convexity, at a point      201
Gage of uniform smoothness      205
Gage of uniform smoothness, of the norm      231
Gage of uniform smoothness, on a set      204
Global error bound      262 265
Graph of multifunction      12
Half-space, closed      5
Half-space, open      5
Hull, affine      2
Hull, conic      2
Hull, conic, closed      7
Hull, convex      2
Hull, convex, closed      7
Hull, linear      2
Hull, lsc convex      63
Hyperplane, closed      5
Hyperplane, supporting      5
Image of multifunction      12
Interior, algebraic      3
Interior, algebraic, relative      3
Interior, algebraic, with respect to      2
Interior, quasi relative      15
Kadec — Klee property      233
Kadec — Klee property, weak*      233
Lagrange multiplier      139 140
Lagrangian      138
Lsc envelope      62
Lsc regularization      62
Max-convolution      43
Metrically regular system      269
Minkowski gauge      4
Multifunction      12
Multifunction, bcs-complete      13
Multifunction, closed      13
Multifunction, cs-complete      13
Multifunction, cs-convex      13
Multifunction, ideally convex      13
Multifunction, inverse      12
Multifunction, lcs-closed      13
Multifunction, li-convex      13
Multifunction, locally, at a point      286
Multifunction, locally, bounded      286
Multifunction, monotone      82
Multifunction, monotone, cyclically      84
Multifunction, monotone, maximal      82
Multifunction, monotone, strictly      82
Normed space, smooth      227
Normed space, strictly convex      227
Operator, Q-concave      42
Operator, Q-convex      42
Operator, relatively open      119
Point, local maximum      105
Point, local minimum      105
Point, saddle      138
Point, sharp minimum      248
Point, support      5
Problem, convex Problem, programming      99
Problem, dual      107
Problem, normal      109
Problem, primal      107
Problem, stable      109
Process      26
Process, adjoint      26
Process, closed      26
Process, convex      26
Quasi-inverse, greatest      188
Quasi-inverse, lowest      188
Semi-norm      4
Separation of two sets      5
Separation of two sets, proper      5
Separation of two sets, strict      5
Series, b-convex      9
Series, Cauchy      9
Series, convergent      9
Series, convex      9
Set, absorbing      4
Set, admissible solutions      99
Set, Affine      1
Set, balanced      1
Set, bcs-complete      9
Set, Chebyshev      237
Set, constraints      99
Set, convex      1
Set, cs-closed      9
Set, cs-complete      9
Set, ideally convex      9
Set, level      39
Set, level, strict      39
Set, lower cs-closed (lcs-closed)      11
Set, lower ideally convex (li-convex)      11
Set, monotone      82
Set, monotone, maximal      82
Set, monotone, strictly      82
Set, polar      7
Set, quasi-continuous      67
Set, star-shaped      1
Set, symmetric      1
Set, weak sharp minima      248
Sets united      17
Slater's condition      138
Solution, $\varepsilon-$      106
Solution, admissible      137
Solution, optimal      99
Space, algebraic dual      3
Space, barreled      9
Space, complete      8
Space, first countable      8
Space, Frechet      8
Space, linear, parallel to      2
Space, orthogonal      7
Space, quasi-complete      8
Space, topological dual      4
Subdifferential      80
Subdifferential, $\varepsilon-$      82
Subdifferential, abstract      178
Subdifferential, Clarke      175
Subdifferential, Fenchel      80
Subgradient      80
Subgradient, $\varepsilon-$      82
Support functional      5
Support point      5
Theorem Alaoglu — Bourbaki      8
Theorem Baire I      34
Theorem Baire II      34
Theorem Banach — Steinhaus      25
Theorem biconjugate      77
Theorem bipolar      7
Theorem Bishop — Phelps      166
Theorem Borwein      159
Theorem Borwein — Preiss      31
Theorem Brondsted — Rockafellar      161
Theorem Closed Graph      25
Theorem Dieudonne      7
Theorem Eidelheit      5
Theorem Ekeland      29
Theorem Ioffe — Tikhomirov      97
Theorem open mapping      25
Theorem Pshenichnyi — Rockafellar      136
Theorem Robinson      23
Theorem Rockafellar      169 288
Theorem Simons      22 167
Theorem Ursescu      23
Theorem Zagrodny      179
Uniformly convex      234
Uniformly convex, locally      234
Uniformly smooth      231
Uniformly smooth, at a point      231
Uniformly smooth, locally      231
Value of a problem      99
Value saddle      144
Young — Fenchel inequality      75
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