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Series Editor Nikolaos Limnios
Convex Optimization
Introductory Course
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:
ISTE Ltd
27-37 St George’s Road
London SW19 4EU
UK
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
© 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
| 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 |