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| Robinson S.M. — Convexity and Monotonicity in Finite-Dimensional Spaces |
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| Предметный указатель |
 (almost equal) 107
 (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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