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Robinson S.M. — Convexity and Monotonicity in Finite-Dimensional Spaces
Robinson S.M. — Convexity and Monotonicity  in Finite-Dimensional Spaces

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Название: Convexity and Monotonicity in Finite-Dimensional Spaces

Автор: Robinson S.M.

Аннотация:

Any book on a well-established subject has to build on the work of others. There is now a vast technical literature on convexity, parts of which we'll reference below in the individual sections of this book. However, it is a pleasure to point out here some excellent works of a more comprehensive nature. These are by no means all such works, but they are works that I have used particularly for study or reference.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 143

Добавлена в каталог: 07.04.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\cong$ (almost equal)      107
$\mathcal{F}\{C\}$ (faces of C)      74
Affine combination      6
Affine hull      7
Affine independence      13
Affine sets, parallel      6
Affine transformation      8
Asymptotic cone      55
Asymptotic cone, representation by limits      56
Barrier cone      64
Barycentric coordinates      21
Boundary, relative      27
Boundedness of an intersection      55
Caratheodory's theorem      19
Characterization of boundedness      55
Characterization of general position      13
Characterization of lower semicontinuity      101
Characterization of recession cone      62
Characterization of separation, proper      43
Characterization of separation, strong      41
Closed halfspace of hyperplane      7
Closed multifunction      132
Closedness of a sum of sets      59
Closedness of linear image      58
Closest point to convex set      34
Closure of a function      105
Closure, lower, of epigraph      127
Combination, affine      6
Cone      45
Cone, asymptotic      55
Cone, barrier      64
Cone, convex      46
Cone, generated by a set      48
Cone, normal      66
Cone, pointed      53
Cone, recession      60
Cone, tangent      66
Conical hull      48
Conjugate, concave      112
Conjugate, convex      111
Constancy space of a convex function      120
Contraction      35
Convex coefficients      16
Convex combination      16
Convex function      91
Convex hull      17
Convex hull, generalized      22
Convex set      16
Coordinates, barycentric      21
Definition of separation      33
Derivative, directional      134
Dimension of an affine set      7
Dimension of convex set      17
Directional derivative      134
Directional derivative and support function      135
Distance      4
Distance between points      4
Distance, point to set      34
Domain, effective      103
Effective domain      103
Effective domain of a multifunction      132
Element, recession      60
Equivalent properties of subdifferential      131
Eventually      4
Extension of a function      100
Extreme point      74
Extreme ray      74
Face of a Cartesian product      77
Face of a convex set      74
Face of a forward linear image      78
Face of a polyhedral convex set      82
Face of an intersection      77
Face of an inverse linear image      76
Face, exposed      75 84
Face, proper      74
Facet of a convex set      88
Finitely generated convex set      81
Frequently      4
Function, convex      91
Function, proper      99
Function, recession      118
Function, strictly convex      91
Function, strongly convex      91
Function, weakly convex      91
Functions, extended-real-valued      98
General position      13
General position, extended      22
Generalized inverse, linear      9
Generalized inverse, Moore — Penrose      11
Generator of halfline      22
Global minimizer      91
Gordan's Theorem      36
Gordan's theorem in matrix form      36
Graph of a multifunction      132
Graph of multifunction      132
Halfline      22
Hyperplane      7
Image of a multifunction      132
Image of matrix      3
Image of multifunction      132
Interior, relative      24
Inverse image of a set      11
Inverse of a multifunction      132
Inverse of multifunction      132
Kernel of matrix      3
Level set of a function      100
Line      7
Lineality space      47
Linear combination, nonnegative      22
Linear programming problems      38
Local minimizer      91
Lower closure of an epigraph      127
Lower semicontinuous      99
Lower semicontinuous hull of a function      101
Matrix      3
Matrix, empty      4
Minimizer, global      91
Minimizer, local      91
Minkowski sum      4
Modulus of convexity      91
Monotone multifunction      132
Multifunction      132
Multifunction, closed      132
Multifunction, monotone      132
Neighborhood system      99
Norm      4
Norm, Euclidean      4
Normal cone      66
Normal to a hyperplane      7
Normal vector      66
Notation      3
Notation for line segment      16
Open halfspace of hyperplane      7
Orthant, nonnegative      3
Orthant, nonpositive      3
Parallel subspace of a convex set      17
Parallel subspace of an affine set      7
Partition of a set      75
Point      7
Point, extreme      74
Points, affinely independent      13
Polar of a set      20
Polyhedral convex set      81
Positive hull      22
Positively homogeneous function      50
Projector      34
Projector, Euclidean      34
Projector, linear      10
Proper function      99
Ray, extreme      74
Recession cone      60
Recession cone and barrier cone of polar      64
Recession cone of a convex function      120
Recession cone, of intersection      62
Recession cone, of inverse linear image      62
Recession element      60
Recession function      118
Relative boundary      27
Relative interior      24
Relatively open set      24
Separation      33
Separation, proper      33
Separation, strict      33
Separation, strong      33
Set, Affine      5
Set, finitely generated convex      81
Set, polyhedral convex      81
Set, relatively open      24
Sets, almost equal      107
simplex      20
Simplex, generalized      23
Simplex, standard      20
Space lineality      47
Special notation for line segments      26
Strictly convex function      91
Strongly convex function      91
Structure of subdifferential      136
Subdifferential mapping      132
Subdifferential of a convex function      131
Subgradient of a convex function      107
Sum, Minkowski      4
Support function      114
Tangent cone      66
Transformation, affine      8
Transpose of matrix      3
Unit ball of norm      4
Unit vectors, standard      3
Upper semicontinuous      99
Vector      3
Vector, empty      4
Vector, nonnegative      3
Vector, normal      66
Vector, positive      3
Vertices of a simplex      20
Vertices of simplex      20
Weakly convex function      91
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