Convex Optimization. Mikhail Moklyachuk

      First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

      Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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      © ISTE Ltd 2020

      The rights of Mikhail Moklyachuk to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

      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

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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