This volume is a collection of papers presented at the Eighth French-German Conference on Optimization held at the University of Trier (Germany) in 1996. From July 21 through July 26, 1996, about 100 scientists, mainly from France and Germany, but also from other countries, met at Trier to discuss recent de- velopments in the field of optimization. 89 lectures were delivered, covering a large range of theoretical and practical aspects of optimization. Most of the talks were scheduled in two parallel sessions, grouped into sections including convex and nonsmooth analysis, methods in convex and nonconvex program- ming, sensitivity and stability analysis, control theory, ill-posed programming problems, equilibrium problems, and global optimization. Continuing an old tradition, the Eighth French-German Conference on Opti- mization demonstrated vividly the vitality of the French-German cooperation in mathematics. The Scientific Committee of the conference consisted of A. Auslender (Paris), H.G. Bock (Heidelberg), S. Dolecki (Dijon), R. Durier (Dijon), J.B. Hiriart- Urruty (Toulouse), H. Th. Jongen (Aachen), D. Klatte (Zurich), B. Kum- mer (Berlin), C. Lemarechal (Rocquencourt), P.Loridan (Paris), C. Mich- elot (Dijon), W. Oettli (Mannheim), D. Pallaschke (Karlsruhe), J.P. Penot (Pau), J. Stoer (Wurzburg), M. Thera (Limoges), L. Thibault (Montpellier), R. Tichatschke (Trier)' J. Zowe (Erlangen).

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.

This volume is a collection of papers presented at the Eighth French-German Conference on Optimization held at the University of Trier (Germany) in 1996. From July 21 through July 26, 1996, about 100 scientists, mainly from France and Germany, but also from other countries, met at Trier to discuss recent de- velopments in the field of optimization. 89 lectures were delivered, covering a large range of theoretical and practical aspects of optimization. Most of the talks were scheduled in two parallel sessions, grouped into sections including convex and nonsmooth analysis, methods in convex and nonconvex program- ming, sensitivity and stability analysis, control theory, ill-posed programming problems, equilibrium problems, and global optimization. Continuing an old tradition, the Eighth French-German Conference on Opti- mization demonstrated vividly the vitality of the French-German cooperation in mathematics. The Scientific Committee of the conference consisted of A. Auslender (Paris), H.G. Bock (Heidelberg), S. Dolecki (Dijon), R. Durier (Dijon), J.B. Hiriart- Urruty (Toulouse), H. Th. Jongen (Aachen), D. Klatte (Zurich), B. Kum- mer (Berlin), C. Lemarechal (Rocquencourt), P.Loridan (Paris), C. Mich- elot (Dijon), W. Oettli (Mannheim), D. Pallaschke (Karlsruhe), J.P. Penot (Pau), J. Stoer (Wurzburg), M. Thera (Limoges), L. Thibault (Montpellier), R. Tichatschke (Trier)' J. Zowe (Erlangen).

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.