Plenary Lecture
Second Order Conditions and Uniqueness of Multipliers in Optimal Control
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Professor Javier F. Rosenblueth
Applied Mathematics and Systems Research Institute
National Autonomous University of Mexico
Mexico
E-mail: jfrl@unam.mx
Abstract: The main purpose of this talk is to present new results related to uniqueness of multipliers derived in first order conditions for certain classes of optimal control problems. The issue arises, for example, in sensitivity analysis of optimization problems or in convergence analysis of optimization algorithms. In nonlinear programming, it is well-known that a strict form of the Mangasarian-Fromovitz constraint qualification is a necessary and sufficient condition for the uniqueness of Kuhn-Tucker multipliers and, moreover, it implies the satisfaction of second order necessary conditions at a local minimum. However, in the case of optimal control problems involving equality and inequality constraints, the situation is much subtler, and we shall explain how the corresponding constraint qualification is no longer equivalent to the uniqueness of multipliers. We discuss new results in this context, including different constraint qualifications proposed and their relation with second order conditions.
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 80 refereed papers, has spent sabbatical visits at the Weizmann Institute of Science, Rehovot, and Technion Israel Institute of Technology, Haifa, Israel, 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.