Convex Optimization. Mikhail Moklyachuk

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      Library of Congress Control Number: 2020943973

      British Library Cataloguing-in-Publication Data

      A CIP record for this book is available from the British Library

      ISBN 978-1-78630-683-8

      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
ℝm × 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
ℂm × 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
λi(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
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