Evenly Convex Sets: Linear Systems Containing Strict Inequalities
This chapter deals with linear systems with an arbitrary (possibly infinite) number of weak and/or strict inequalities and their solution sets, the so-called evenly convex sets, which can be seen as the two faces of a same coin. Section 1.1 provides diffe
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María D. Fajardo Miguel A. Goberna Margarita M.L. Rodríguez José Vicente-Pérez
Even Convexity and Optimization Handling Strict Inequalities
EURO Advanced Tutorials on Operational Research Series Editors M. Grazia Speranza, Brescia, Italy José Fernando Oliveira, Porto, Portugal
The EURO Advanced Tutorials on Operational Research are a series of short books devoted to an advanced topic—a topic that is not treated in depth in available textbooks. The series covers comprehensively all aspects of Operations Research. The scope of a Tutorial is to provide an understanding of an advanced topic to young researchers, such as Ph.D. students or Post-docs, but also to senior researchers and practitioners. Tutorials may be used as textbooks in graduate courses.
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María D. Fajardo • Miguel A. Goberna • Margarita M.L. Rodríguez • José Vicente-Pérez
Even Convexity and Optimization Handling Strict Inequalities
María D. Fajardo Department of Mathematics University of Alicante Alicante, Spain
Miguel A. Goberna Department of Mathematics University of Alicante Alicante, Spain
Margarita M.L. Rodríguez Department of Mathematics University of Alicante Alicante, Spain
José Vicente-Pérez Department of Mathematics University of Alicante Alicante, Spain
ISSN 2364-687X ISSN 2364-6888 (electronic) EURO Advanced Tutorials on Operational Research ISBN 978-3-030-53455-4 ISBN 978-3-030-53456-1 (eBook) https://doi.org/10.1007/978-3-030-53456-1 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This is the first book devoted to linear systems of the form: σ = {at , x ≤ bt , t ∈ W ; at , x < b
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