Lecture Notes in Economics and Mathematical Systems 563

Founding Editors: M. Beckmann H. P. Kunzi

Managing Editors: Prof. Dr. G. Fandel FachbereichWirtschaftswissenschaften Femuniversitat Hagen Feithstr. 140/AVZII, 58084 Hagen, Germany Prof. Dr. W. Trockel Institut fur Mathematische Wirtschaftsforschung (IMW) Universitat Bielefeld Universitatsstr. 25, 33615 Bielefeld, Germany

Editorial Board: A. Basile, A. Drexl, H. Dawid, K. Inderfurth, W. Kursten, U. Schittko Alberto Seeger (Ed.)

Recent Advances in Optimization

Spri nger Editor Prof. Alberto Seeger University of Avignon Department of Mathematics 33, rue Louis Pasteur 84000 Avignon, France E-mail: [email protected]

ISSN 0075-8442 ISBN-10 3-540-28257-2 Springer Berlin Heidelberg New York ISBN-13 978-3-540-28257-0 Springer Berlin Heidelberg New York

This work is subject to copyright. AH rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline. com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, 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. Typesetting: Camera ready by author Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper 42/3130Jo 5 4 3 2 10 Preface

This volume contains the Proceedings of the Twelfth French-German-Spanish Conference on Optimization held at the University of Avignon in 2004. We refer to this conference by using the acronym FGS-2004. During the period September 20-24, 2004, about 180 scientists from around the world met at Avignon (France) to discuss recent developments in optimization and related fields. The main topics discussed during this meeting were the following: 1. smooth and nonsmooth continuous optimization problems, 2. numerical methods for mathematical programming, 3. optimal control and calculus of variations, 4. differential inclusions and set-valued analysis, 5. stochastic optimization, 6. multicriteria optimization, 7. game theory and equilibrium concepts, 8. optimization models in finance and mathematical economics, 9. optimization techniques for industrial applications.

The Scientific Committee of the conference consisted of F. Bonnans (Rocquen- court, France), J.-B. Hiriart-Urruty (Toulouse, France), F. Jarre (Diisseldorf, Germany), M.A. Lopez (Alicante, Spain), J.E. Martinez-Legaz (Barcelona, Spain), H. Maurer (Miinster, Germany), S. Pickenhain (Cottbus, Germany), A. Seeger (Avignon, France), and M. Thera (Limoges, France). The conference FGS-2004 is the 12th of the series of French-German meetings which started in Oberwolfach in 1980 and was continued in Confolant (1981), Luminy (1984), Irsee (1986), Varetz (1988), Lambrecht (1991), Dijon (1994), Trier (1996), Namur (1998), Montpellier (2000), and Cottbus (2002). Since 1998, this series of meetings has been organized under the participation of a third European country. In 2004, the guest country was Spain. The con­ ference promoted, in particular, the contacts between researchers of the three VI Preface involved countries and provide a forum for sharing recent results in theory and applications of optimization. The conference FGS-2004 was organized by the "Group of Nonlinear Analysis and Optimization" of the University of Avignon. As chairman of the Orga­ nizing Committee, I would like to acknowledge the following institutions for their financial or material support: • Region Provence-Alpes-Cote d'Azur • Universite d'Avignon et des Peiys de Vaucluse • Agroparc: Technopole Regional d'Avignon • Mairie d'Avignon • Institut National de Recherche en Informatique et en Automatique

For the sake of convenience, the contributions appearing in this volume are splitted in four different groups: Part I. Optimization Theory and Algorithms, Part II. Optimal Control and Calculus of Variations, Part III. Game Theory, Part IV. Modeling and Numerical Testing. Each contribution has been examined by one or two referees. The evaluation process has been more complete and thorough for the contributions appear­ ing in Parts I, II, and III. The papers in Part IV are less demanding from a purely mathematical point-of-view (no theorems, propositions, etc). Their principal concern is either the modeling or the computer resolution of specific optimization problems arising in industry and applied sciences.

I would like to thank all the contributors for their effort and the anony­ mous referees for their comments and suggestions. The help provided by Mrs Monique Lefebvre (Secretarial Office of FGS-2004) and the staff of Springer- Verlag is also greatly appreciated.

Avignon, September 2005 Alberto Seeger Contents

Part I Optimization Theory and Algorithms

On the Asymptotic Behavior of a System of Steepest Descent Equations Coupled by a Vanishing Mutual Repulsion F. Alvarez, A. Cabot 3 Inverse Linear Programming S. Dempe, S. Lohse 19 Second-Order Conditions in C^'^ Vector Optimization with Inequality and Equality Constraints Ivan Ginchev, Angela Guerraggio, Matteo Rocca 29 Benson Proper Efficiency in Set-Valued Optimization on Real Linear Spaces E. Hernandez, B. Jimenez and V. Novo 45 Some Results About Proximal-Like Methods A. Kaplan, R. Tichatschke 61 Application of the Proximal Point Method to a System of Extended Primal-Dual Equilibrium Problems Igor V. Konnov 87 On Stability of Multistage Stochastic Decision Problems Alexander Mdnz, Silvia Vogel 103 Nonholonomic Optimization C. Udri§te, O. Dogaru, M. Ferrara, I. T^vy 119 A Note on Error Estimates for some Interior Penalty Methods A. F. Izmailov, M. V. Solodov 133 VIII Contents

Part II Optimal Control and Calculus of Variations

L^—Optimal Boundary Control of a String to Rest in Finite Time Martin Gugat 149 An Application of PL Continuation Methods to Singular Arcs Problems Pierre Martinon and Joseph Gergaud 163 On an Elliptic Optimal Control Problem with Pointwise Mixed Control-State Constraints Christian Meyer, Fredi Troltzsch 187 On Abstract Control Problems with Non-Smooth Data Zsolt Pales 205 Sufficiency Conditions for Infinite Horizon Optimal Control Problems Sabine Pickenhain, Valeriya Lykina 217 On Nonconvex Relaxation Properties of Multidimensional Control Problems Marcus Wagner 233 Existence and Structure of Solutions of Autonomous Discrete Time Optimal Control Problems Alexander J. Zaslavski 251 Numerical Methods for Optimal Control with Binary Control Functions Applied to a Lot ka-Volt err a Type Fishing Problem Sebastian Sager, Hans Georg Bock, Moritz Diehl, Gerhard Reinelt, Johannes P. Schloder 269

Part III Game Theory

Some Characterizations of Convex Games Juan Enrique Martmez-Legaz 293 The Bird Core for Minimum Cost Spanning Tree Problems Revisited: Monotonicity and Additivity Aspects Stef Tijs, Stefano Moretti, Rodica Branzei, Henk Norde 305 A Parametric Family of Mixed Coalitional Values Francesc Carreras, Maria Albina Puente 323 Contents IX

Part IV Industrial Applications and Numerical Testing

Complementarity Problems in Restructured Natural Gas Markets Steven Gabriel, Yves Smeers 343

Reconciling Franchisor and l^Vanchisee: A Planar Biobjective Competitive Location and Design Model Jose Fernandez, Bogldrka Toth, Frank Plastria, Bias Pelegrin 375

Tools for Robotic Trajector^'^ Planning Using Cubic Splines and Semi-Infinite Programmiing A. Ismael F. Vaz, Edite M,G.P. Fernandes 399

Solving Mathematical Programs with Complementarity- Constraints with Nonlinear Solvers Helena Sofia Rodrigues, M. Teresa T. Monteiro 415

A Filter Algorithm and Other NLP Solvers: Performance Comparative Analysis Antonio Sanches Antunes, M. Teresa T. Monteiro 425

How Wastewater Processes can be Optimized Using LOQO LA. C. P. Espirito-Santo, Edite M. G. P. Fernandes, M. M. Araujo, E. C. Ferreira 435 List of Contributors

Felipe Alvarez Francesc Carreras Universidad de Chile/Departamento Polytechnic University of Catalonia/ de Ingenieria Matematica and Centre Dep. of Applied Mathematics II and de Modelamiento Matematico Industrial Engineering School Casilla 170/3, Correo 3 Terrassa, Spain Santiago, Chile f reuacesc. carrerasQupc. edu falvarezQdim.uchile.cl Antonio Sanches Antunes Stephan Dempe University of Minho Tech. University Bergakademie Portugal Freiberg/Dep. of Mathematics and [email protected] Computer Sciences Akademiestr. 6 M. Madalena Araujo 09596 Freiberg, Germany Minho University/Systems and dempeSmath.tu-freiberg.de Production Department Braga, Portugal mmarauj oQdps.uminho.pt Moritz Diehl IWR Heidelberg Rodica Branzei Heidelberg, Germany Alexandru loan Cuza Univer­ sity/Faculty of Computer Science Oltin Dogaru lasi, Romania University Politehnica of Bucharest/ branzeirQinfo.uaic.ro Department of Mathematics Hans Georg Bock Splaiul Independen^ei 313 IWR Heidelberg 060042 Bucharest, Romania Heidelberg, Germany Alexandre Cabot Isabel A.C.P. Espiritu-Santo Universite de Limoges/Laboratoire Minho University/Systems and LACO Production Department Limoges, France Braga, Portugal [email protected] iapinhoQdps.uminho.pt XII List of Contributors

Edite M.G.P. Fernandes Angelo Guerraggio Universidade do Minho Campus de University of Insubria/Department Gualtar/Departamento de Producao of Economics e Sistemas, Escola de Engenharia Via Ravasi 2 4710-057 Braga, Portugal 21100 Varese, Italy emgpfQdps.uminho.pt aguerraggioQeco.uninsubria.it Martin Gugat Jose Fernandez Universitat Erlangen- University of Murcia/Dep. Statistics Niirnberg/Lehrstuhl 2 fiir Ange- and Operations Research wandte Mathematik Murcia, Spain Martensstr. 3 91058 Erlangen, Germany Massimiliano Ferrara gugatOam.uni-erlangen.de University of Messina/Faculty of Economics Elvira Hernandez Via dei Verdi 75 UNED/ Depto. de Matematica 98122 Messina, Italy Aplicada, E.T.S.I. Industrials mferraraQunime.it c/ Juan del Rosal 12 28040 Madrid, Spain ehernandezQind.uned.es Eugenio C. Ferreira Minho University/Centre of Biologi­ Alexey F. Izmailov cal Engineering Moscow State University/ Braga, Portugal Dep. of Operations Research ecferreiraQdeb.uminho.pt Leninskiye Gori, GSP-2 119992 Moscow, Russia Steven Gabriel izmafQccas.ru University of Maryland, College Bienvenido Jimenez Park/Department of Civil and Universidad de Salamanca/Depto. Environmental Engineering de Economia e Historia Economica, 20742 Maryland, U.S.A. Facultad de Economia y Empresa sgabrielOumd.edu Campus Miguel de Unamuno, s/n, 37007 Salamanca, Spain Joseph Gergaud bj imenlQencina.pntic.mec.es ENSEEIHT-IRIT/UMR CNRS 5505 2, rue Camichel Alexander Kaplan 31071 Toulouse, France University of Trier/Department of gergaudSenseeiht.fr Mathematics 54286 Trier, Germany Al.KaplanOtiscali.de Ivan Ginchev Technical University of Varna/Dep. Igor V. Konnov of Mathematics Kazan University/Department of Studentska Str. 1 Applied Mathematics 9010 Varna, Bulgaria Kazan, Russia ginchevQmsS.tu-varna.acad.bg ikonnovQksu.ru List of Contributors XIII

Valeriya Lykina Henk Norde Brandenburg Univ. of Technology Tilburg University/CentER and Cottbus, Germany Department of Econometrics and lykinaQmath.tu-cottbus.de Operations Research Tilburg, The Netherlands Sebastian Lohse [email protected] Tech. University Bergakademie Freiberg/Dep. of Mathematics and Computer Sciences Vicente Novo Akademiestr. 6 UNED/ Depto. de Matematica 09596 Freiberg, Germany Aplicada, E.T.S.I. Industriales c/ Juan del Rosal 12 Alexander Manz 28040 Madrid, Spain ASPECTA Lebensversicherung AG vnovoOind.uned.es Germany AMaenzQaspecta.com Zsolt Pales University of Debrecen/Institute of Juan Enrique Martinez-Legaz Mathematics Universitat Autonoma de 4029 Debrecen, Pf. 12, Hungary Barcelona/Departament d'Economia palesQmath.kite.hu i d'Historia Economica 08193 Bellaterra, Spain juanenrique.martinezQuab.es Bias Pelegrin University of Murcia/Dep. Statistics Pierre Martinon and Operations Research ENSEEIHT-IRIT/UMR CNRS 5505 Murcia, Spain 2, rue Camichel 31071 Toulouse, France Sabine Pickenhain martinonQenseeiht.fr Brandenburg Univ. of Technology Christian Meyer Cottbus, Germany Technische Universitat sabineQmath.tu-cottbus.de Berlin/Institut fur Mathematik Str. des 17. Juni 136 Frank Plastria D-10623 Berlin, Germany Vrije Universiteit Brussel/MOSI- cmeyerOmath.tu-berlin.de Dep. of Mathematics, Operational Research and Information Systems M. Teresa T. Monteiro for Management University of Minho Brussel, Belgium Portugal tmOdps.uminho.pt Maria Albina Puente Stefano Moretti Polytechnic University of Catalonia/ University of Genoa/Department of Dep. of Applied Mathematics III and Mathematics Polytechnic School Genoa, Italy Manresa, Spain morettiQdima.unige.it m.albina.puenteQupc.edu XIV List of Contributors

Gerhard Reinelt Rainer Tichatschke IWR Heidelberg University of Trier/Department of Heidelberg, Germany Mathematics 54286 Trier, Germany Matteo Rocca tichatOuni-trier.de University of Insubria/Department of Economics Via Ravasi 2 Stef Tijs 21100 Varese, Italy Tilburg University/CentER and mroccaQeco.uninsubria.it Department of Econometrics and Operations Research Helena Sofia Rodrigues Tilburg, The Netherlands University of Minho [email protected] Portugal helena.rodriguesOipb.pt Boglarka Toth University of Murcia/Dep. Statistics Sebastian Sager and Operations Research IWR Heidelberg Murcia, Spain Heidelberg, Germany Sebastian.sager Oiwr.uni-heidelberg.de Fredi Troltzsch Technische Universitat Joliannes P. Schloder Berlin/Institut fiir Mathematik IWR Heidelberg Str. des 17. Juni 136 Heidelberg, Germany D-10623 Berlin, Germany troeltzQmath.tu-berlin.de Yves Smeers Universite catholique de Louvain/ Dep. of Mathematical Engineering Constantin Udri§te and Center for Operations Research University Politehnica of Bucharest/ and Econometrics Department of Mathematics Louvain-la-Neuve, Belgium Splaiul Independen^ei 313 smeersOcore.ucl.ac.be 060042 Bucharest, Romania udristeQmathem.pub.ro Mikhail V. Solodov Instituto de Matematica Pura e A. Ismael F. Vaz Aplicada Universidade do Minho Campus de Estrada Dona Castorina 110, Jardim Gualtar/Departamento de Producao Botanico, e Sistemas, Escola de Engenharia, RJ 22460-320, Rio de Janeiro, Brazil. 4710-057 Braga, Portugal solodovOimpa.br ai vazOdps. ximinho. pt lonel T^vy University Politehnica of Bucharest/ Silvia Vogel Department of Mathematics Technische Universitaet Ilmenau Splaiul Independen^ei 313 Ilmenau, Germany 060042 Bucharest, Romania Silvia.VogelQtu-ilmenau.de List of Contributors XV

Marcus Wagner Alexander J. Zaslavski Cottbus University of Technol­ Technion, Dep. of Mathematics ogy/Dep. of Mathematics Haifa, Israel Karl-Marx-Str. 17, P.O. Box 101344 aj zaslQtechunix.technion.ac.il D-03013 Cottbus, Germany wagnerQmath.tu-cottbus.de Part I

Optimization Theory and Algorithms