Emphasis on intuitive presentation of ideas underlying various algorithms rather than detailed description of computer codes. Emphasis throughout on recent theoretical development in the field. Emphasis on geometricinsight. Topics include least square optimization of linear systems, minimum norm problems in Banach space, linearization in Hilbert space, iterative solution of system equations and optimization problems. Broad range of applications in operations research and system engineering including control theory, mathematical programming, econometrics, statistical estimation, circuit theory and numerical analysis.
Laboratory develops skill in implementing methodology.
505 Introduction to graph theory and network theory. 531 Stability of equilibrium points for nonlinear systems. Unconstrained and constrained optimal control problems. Pontryagin's maximum principle and dynamic programming. Computation with gradient methods and Newton methods.