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Оглавление

Notations

ℕ	Set of natural numbers
ℤ	Set of integer numbers
ℤ₊	Set of non-negative integer numbers
ℝ	Set of real numbers
	Extended set of real numbers
ℚ	Set of rational numbers
ℝⁿ	Set of real n-vectors
ℝ^{m × n}	Set of real m × n-matrices
ℝ₊	Set of non-negative real numbers
ℝ₊₊	Set of positive real numbers
ℂ	Set of complex numbers
ℂⁿ	Set of complex n-vectors
ℂ^{m × n}	Set of complex m × n-matrices
	Set of symmetric n × n-matrices
	Set of symmetric positive semidefinite n × n-matrices
	Set of symmetric positive definite n × n-matrices
	Identity matrix
X ^⊤	Transpose of matrix X
tr (X)	Trace of matrix X
λ_i(X)	ith largest eigenvalue of symmetric matrix X
〈· , ·〉	Inner product
x ⊥ y	Vectors x and y are orthogonal: 〈x, y〉 = 0
V ^⊥	Orthogonal complement of subspace V
diag(X)	Diagonal matrix with diagonal entries x₁, … , xn
rank (X)	Rank of matrix X
‖·‖	A norm
‖·‖_*	Dual of norm ‖·‖
‖ x ‖₂	Euclidean norm of vector x
x ⪯ y	Componentwise inequality between vectors x and y
x ≺ y	Strict componentwise inequality between vectors x and y
X ⪯ Y	Matrix inequality between symmetric matrices X and Y
X ≺ Y	Strict matrix inequality between symmetric matrices X and Y
X ⪯_K Y	Generalized inequality induced by proper cone K
X ≺_K Y	Strict generalized inequality induced by proper cone K
int X	Interior of set X
ri X	Relative interior of set X
conv X	Convex hull of set X
aff X	Affine hull of set X
cone X	Conic hull of set X
Lin X	Linear hull of set X
	Closure of set X
	Closed convex hull of set X
dim X	Dimension of set X
∂ X	Boundary of set X
K ^*	Dual cone associated with cone K
	A ray proceeding from a point in the direction h
Hpβ	A hyperplane with the normal vector p
	Half-spaces generated by hyperplane Hpβ
π_X(a)	Projection of point a onto set X
ρ(X₁, X₂)	Distance between sets X₁ and X₂
epi f	Epigraph of function f
Sr (f)	Sublevel set of function f
dom f	Effective set of function f
f₁ ⊕ f₂	Infimal convolution of functions f₁, f₂
μ(x\X)	Minkowski function
γX(x)	Gauge function
δ(x\X)	Indicator function
σ(x\X)	Support function
f ^*	Conjugate function
∂f(x)	Subdifferential of function f at point x
	Superdifferential of function f at point x
∏(ℝ^m)	Set of all non-empty subsets of the space ℝ^m

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