Nonlinear Optimization and Related Topics
This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In th
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Applied Optimization Volume 36 Series 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 of this volume.
Nonlinear Optimization and Related Topics edited by
Gianni Di Pillo University Di Roma La Sapienza
and Franco Giannessi University of Pisa
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library ofCongress Cataloging-in-Publication Data
Nonlinear optimization and related topics / edited by Gianni Di PiUo and Franco Giannessi. p. cm. -- (Applied optimization ; v. 36) ISBN 978-1-4419-4823-6 ISBN 978-1-4757-3226-9 (eBook) DOI 10.1007/978-1-4757-3226-9 1. Mathematical optimization--Congresses. 2. Nonlinear theories--Congresses. 1. Oi Pillo, G. II. Giannessi, F. ill. Workshop on Nonlinear Optimization (1998 : Erice, Italy) IV. Applied optimization; voI. 36. QA402.5 .N55 1999 99-056953 ISBN 978-1-4419-4823-6
Printed on acid-free paper
AII Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1st edition 2000 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
Contents Preface
vii
Generalized Lagrange multipliers: regularity and boundedness Giancarlo Bigi, Massimo Pappalardo
1
A primal-dual algorithm for minimizing a non-convex function subject to bound and 15 linear equality constraints Andrew R. Conn, Nicholas 1. M. Gould, Philippe L. Toint Minimal convexificators of a positively homogeneous function and a characterization 51 of its convexity and concavity Vladimir F. Demyanov Optimal control problems and penalization Vladimir F. Demyanov, Franco Giannessi, Vladimir V. Karelin
67
A truncated Newton method for constrained optimization Gianni Di Pillo, Stefano Lucidi, Laura Palagi
79
Fixed and virtual stability center methods for convex nonsmooth minimization 105 Antonio Fuduli, Manlio Gaudioso Iterative methods for ill-conditioned linear systems from optimization Nicholas I. M. Gould
123
An algorithm for solving nonlinear programs with noisy inequality constraints Michael Hintermiiller
143
Generic existence, uniqueness and stability in optimization problems Alexander Ioffe, Roberto Lucchetti
169
On a class of bilevel programs Martine Labbe, Patrice Marcotte, Gilles Savard
183
Separation methods for vector variational inequalities. Saddle point and gap function Giandomenico Mastroeni
207
Functions with primal-dual gradient structure and U-Hessians Robert Mijfiin, Claudia Sagastizabal
219
Quadratic and multidimensional assignment problems Panos M. Pardalos, Leonidas S. Pitsoulis
235
A new merit function and an SQP method for non-strictly monotone variational inequalities 257 Michael Patriksson v
A logarithmic barrier approach to Fischer function Jiming Peng,
