Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty fun
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Applied Optimization Volume 22 Series Editors:
Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University ofFlorida, U.S.A.
The titles published in this series are listed at the end of this volume.
Refonnulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods Edited by
Masao Fukushima Kyoto University, Kyoto, Japan
and
Liqun Qi The University o/New South Wales, Sydney, Australia
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4419-4805-2 ISBN 978-1-4757-6388-1 (eBook) DOI 10.1007/978-1-4757-6388-1
Printed on acid-free paper
All Rights Reserved © 1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999 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
Solving Complementarity Problems by Means of a New Smooth Constrained Nonlinear Solver Roberto Andreani and Jose Mario Martinez
1
c-Enlargements of Maximal Monotone Operators: Theory and Applications Regina S. Burachik, Claudia A. Sagastizdbal and B. F. Svaiter
25
A Non-Interior Predictor-Corrector Path-Following Method for LCP James V. Burke and Song Xu
45
Smoothing Newton Methods for Nonsmooth Dirichlet Problems Xiaojun Chen, Nami Matsunaga and Tetsuro Yamamoto
65
Frictional Contact Algorithms Based on Semismooth Newton Methods Peter W. Christensen and Jong-Shi Pang
81
Well-Posed Problems and Error Bounds in Optimization Sien Deng Modeling and Solution Environments for MPEC: GAMS Steven P. Dirkse and Michael C. Ferris
117
8£ MATLAB
127
Merit Functions and Stability for Complementarity Problems Andreas Fischer
149
Minimax and Triality Theory in Nonsmooth Variational Problems David Yang Gao
161
Global and Local Superiinear Convergence Analysis of Newton-Type Methods for Semismooth Equations with Smooth Least Squares Houyuan Jiang and Daniel Ralph
181
Inexact Trust-Region Methods for Nonlinear Complementarity Problems Christian Kanzow and Martin Zupke
211
vi
REFORMULATION
Regularized Newton Methods for Minimization of Convex Quadratic Splines with Singular Hessians
235
Wu Li and John Swetits
Regularized Linear Programs with Equilibrium Constraints
259
Olvi L. Mangasarian
Reformulations of a Bicriterion Equilibrium Model
269
Patrice Marcotte
A Smoothing Function and its Applications
293
Ji-Ming Peng
On the Local Super-Linear Convergence of a Matrix Secant Implementation of the Variable Metric Proximal Point Algorithm for Monotone Operators
317
Maijian Qian and James V. Burke
Reformulation of a Problem of Economic Equilibrium
335
Alexander M. Rubinov and Bevil M. Glover
A Globally Convergent Inexact Newton Method for Systems of Monotone Equations
355
Michael V. Solodov and Benar F. Svaiter
On the Limiting Behavior
