Ill posed Variational Problems and Regularization Techniques

Developments in the field of ill-posed variational problems and variational inequalities are presented here. The work covers a large range of theoretical, numerical and practical aspects. This volume is a collection of papers presented at the Workshop on fll-Posed Variational Problems and Regularization Techniques held at the University of Trier (Germany) in September 1998. From September 3 through September 5, 1998, about 50 scientists met at Trier to discuss recent developments in the field of ill-posed variational prob- lems and variational inequalities. 17 lectures were delivered, covering a large range of theoretical, numerical and practical aspects. The topics, as well as the invited speakers, were selected by the organizers. The main topics dis- cussed were o Regularization methods for equilibrium problems o Variational inequalities and complementarity problems and their reg- ularization o Regularization of fixed point problems o Links between approximation, penalization and regularization o Bundle methods, nonsmooth optimization and regularization o Error bounds for regularized optimization problems The organizers are gratful to all participants for their contribution to the success of this workshop. We also wish to express our cordial thanks for the financial support granted by the Deutsche Forschungsgemeinschajt, Bonn and the University of Trier. We are indebted to the referees for their helpful comments and suggestions and to our colleagues of the University Trier for their assistance in preparing this volume. M. Thera, U niversite de Limoges (France) R. Tichatschke, University of Trier (Germany) Contents Antipin A. , Vasil'ev F. Regularization Method for Equilibrium Programming Problem with Inaccurate Initial Data ...1 Attouch H. , Champion T. LP-Regularization of the Non-Parametric Minimal Surface Problem ...25 Auslender A. , Teboulle M. , Ben-Tiba S.