Plenary Lecture
Implications between Different Constraint Qualifications in Calculus of Variations
Professor Javier F. Rosenblueth
Applied Mathematics and Systems Research Institute
National Autonomous University of Mexico
Mexico City
MEXICO
E-mail: jfrl@unam.mx
Abstract: Constraint qualifications for mathematical programming problems correspond to nondegeneracy conditions in the Fritz John optimality condition, assuring the positiveness of the cost multiplier and thus yielding the Karush-Kuhn-Tucker optimality conditions or first order Lagrange multiplier rule. They play a fundamental role in the derivation of both first and second order necessary conditions, and different implications between them are well-known in the literature. In this talk we shall give a brief overview of the main constraint qualifications known for problems in the calculus of variations involving equality and inequality constraints, which have their counterpart in the finite dimensional case, and show that, surprisingly, some of the corresponding implications may no longer be true.
Brief Biography of the Speaker: Professor Rosenblueth holds a BSc in Mathematics from the National Autonomous University of Mexico and a PhD in Control Theory from the Imperial College of Science, Technology and Medicine, London, UK. He worked as a researcher in the Centre for Research in Mathematics, Guanajuato, Mexico and, since 1989, joined the Applied Mathematics and Systems Research Institute of the National Autonomous University of Mexico. He is Full Professor and currently a member of the Mathematical Physics Department. He has published more than 85 refereed papers, has spent sabbatical visits at the Weizmann Institute of Science, Rehovot, and Technion Israel Institute of Technology, Haifa, Israel; Imperial College and University of Bath, UK; University of Porto, Portugal, amongst others. He is associate editor of several refereed journals, and has participated in numerous international conferences. His main research interests are in optimal control theory, calculus of variations, variational analysis and optimization.