Speaker：Prof. Kok Lay Teo（Curtin University, Western Australia）
Title:omputational Approach to a Class of Stochastic Impulsive Optimal Parameter Selection Problems
Time: April, 25 14：30--15：30
Place: Room 422 of School of Mathematics and Statistics
In this talk, we consider a class of stochastic optimal parameter selection problems, where its dynamics are described by a system of linear Ito stochastic differential equations with state jumps. The times at which the jumps occurred as well as their heights are decision variables. This stochastic impulsive optimal parameter selection problem is subject to probabilistic constraints on the state. We show that this constrained stochastic impulsive optimal parameter selection problem is equivalent to a deterministic impulsive optimal parameter selection problem with its dynamics described by deterministic impulsive differential equations subject to continuous state inequality constraints, where the times at which the jumps occurred as well as their heights remain as decision variables. Then, by introducing a time scaling transform, we show that this constrained deterministic impulsive optimal parameter selection problem is transformed into an equivalent constrained deterministic impulsive optimal parameter selection problem with the jump times being fixed. A constraint transcription technique is then used to approximate the continuous state inequality constraints by a sequence of canonical inequality constraints. This leads to a sequence of approximate deterministic impulsive optimal parameter selection problems subject to canonical inequality constraints. For each of these approximate problems, we derive the gradient formulas of the cost function and the constraint functions. On this basis, an efficient computational method is developed.
Prof Kok Lay Teoreceived his Ph.D. degree in electrical engineering from the University of Ottawa, Canada. He was with the Department of Applied Mathematics, University of New South Wales, Australia, the Department of Industrial and Systems Engineering, National University of Singapore, the Department of Mathematics, the University of Western Australia, Australia. In 1996, he joined the Department of Mathematics and Statistics, Curtin University of Technology, Australia, as Professor. He then took up the position of Chair Professor of Applied Mathematics and Head of Department of Applied Mathematics at the Hong Kong Polytechnic University, China, from 1999 to 2004. He was Professor of Applied Mathematics and Head of Department of Mathematics and Statistics at Curtin University of Technology from 2005 to 2010. He is currently John Curtin Distinguished Professor (the highest rank professor) at Curtin University. He has published 5 books and over 400 journal papers. He has a software package, MISER3.3, for solving general constrained optimal control problems. He is Editor-in-Chief of the Journal of Industrial and Management Optimization, Numerical Algebra, Control and Optimization, and Dynamics of Continuous, Discrete and Impulsive Systems, Series B. He is a Regional Editor of Nonlinear Dynamics and Systems Theory. He also serves as an associate editor of a number of international journals, including Automatica, Journal of Global Optimization, Journal of Optimization Theory and Application, Optimization and Engineering, Discrete and Continuous Dynamic Systems, Dynamics of Continuous, Discrete and Impulsive Systems (Series A), and Optimization Letters. His research interests include both the theoretical and practical aspects of optimal control and optimization, and their practical applications such as in signal processing in telecommunications, and financial portfolio optimization.