Non-Connected Convexities and Applications
Lectori salutem! The kind reader opens the book that its authors would have liked to read it themselves, but it was not written yet. Then, their only choice was to write this book, to fill a gap in the mathematicalliterature. The idea of convexity has app
- PDF / 31,496,505 Bytes
- 375 Pages / 436.812 x 666.096 pts Page_size
- 48 Downloads / 170 Views
Applied Optimization Volume 68
Se ries Editors: Panos M. Pardalos University of Florida, U.s.A. Donald Hearn University of Florida, U.S.A.
The titles published in this series are listed at the end af this va/urne.
Non-Connected Convexities and Applications by
Gabriela Cristescu Aurel Vlaicu University of Arad, Arad, Romania
and
Liana Lup§a Babq-Bolyai University of Cluj-Napoca, Cluj-Napoca, Romiinia
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4613-4881-8
ISBN 978-1-4615-0003-2 (eBook)
DOI 10.1007/978-1-4615-0003-2
Printed on acid-free paper
All Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exeeption of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
This book is dedicated to our families CLEOPATRA and MlliAI CRISTESCU and NICOLAE, LUCIANA and RADU LUP~A
Table of Contents
vii
Table of contents Preface Acknowledgements Main notations
xiii
xvii xix
Part 1. Non-connected convexity properties
1
Tbe fields of non-connected convexity properties
3
1.1
4
1.2
1.3 1.3.1 1.3.2 1.3.3
1.3.4 1.3.5 1.3.6
1.4 1.5
1.6
Classical convexity for sets and the connectivity Axiomatic convexity Convexities defined by segmential methods Convexity in non-linear structures Convexity obtained by restricting the straight-line segment to a part of it Convexity obtained by special straight-li ne segments Convexity obtained by special conditions on straightline segments Convexity obtained by putting the straight-line segments in relation with special external points Weak segmential approach Unions of convex sets Intersectional approach Separational approach vii
5 9 10
13 14
15 16 17 17 19
20
viii 2
Table 01 contents
Convexity witb respect to a set
23
2.1 2.2
24
2.3 2.4 2.5 2.6 2.7 2.8 3
4
28 30 35 41 44 47 54
Bebaviours. Convexity witb respect to a bebaviour
61
3.1 3.2 3.3 3.4 3.5 3.6
The notion of behaviour Properties of classes of behaviours Sequences of behaviours Convexity with respect to a behaviour Convexity space Approximation of the convexity
62 69 75 79 83 86
Convexity witb respect to a set and two behaviours
89
4.1 4.2 4.3 4.4 4.5 5
Types of convexity with respect to a given set Properties of strong n-convex sets and of slack nconvex sets with respect to a given set Properties of strong convex sets and of slack convex sets with respect to a given set Topology with respect to a given set The problem ofbest approximation Separation of strong and slack convex sets Integer convex sets and integer polyhedral sets Convexity space with respect to a given set
Convexity with respect
