Plenary Lecture

Normality and Regularity, Two Constraint Qualifications in Optimal Control

Professor Javier F. Rosenblueth
Applied Mathematics and Systems Research Institute
National Autonomous University of Mexico

Abstract: In nonlinear programming, it is well-known that a cornerstone for establishing second order necessary conditions for optimality is the fact that normality and the Mangasarian-Fromovitz constraint qualification are equivalent, and they in turn imply a regularity condition in the sense that the tangent cone and the set of tangential constraints coincide. In this talk we shall explain how, for optimal control problems involving equality and inequality constraints in the control functions, one can derive second order conditions in terms of the tangent cone, but a striking result occurs: the implication mentioned above between normality and regularity may fail to hold.

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.

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