Theory and Computation for ODE/PDE-constrained optimization
Term: Spring 2004
Course: ENM 520 001
Day/Time: Mondays & Wednesdays 1:30--3:00 PM
This course introduces the basic theory and algorithms for nonlinear
optimization of continuum systems. Emphasis will be given on
numerical algorithms that are applicable to problems in which the
constraints are ordinary or partial differential equations. Such
problems have numerous applications in science and
engineering. Lectures and homework will examine examples related to
control, design, and inverse problems in vision, robotics, computer
graphics, bioengineering, fluid and solid mechanics, molecular
dynamics, and geophysics.
Homeworks (80%) and final project (20%).
Students can use software of their choice;
I recommend MATLAB.
None, but the following texts are recommended for nonlinear
programming and numerical methods for ODEs and PDEs.
Jorge Nocedal, Stephen Wright
Engineering Library QA402.5 .N62
Finite elements : an introduction (out of print)
Eric B. Becker, Graham F. Carey, and J. Tinsley Oden. v.1
Engineering Library TA347.F5 B4
Computer Methods for Ordinary
Differential Equations and Differential-Algebraic Equations
Uri Ascher and Linda Petzold
- Unconstrained Optimization
Newton, Quasi-Newton methods
Least Squares and Gauss-Newton methods
Line search, Trust Region methods
- Constrained Optimization
Sequential Quadratic Programming
Reduced and full space methods
Interior point methods
Boundary and Distributed parameter control
Inverse problems and regularization
Prerequisites Numerical analysis, basic theory of ordinary
and partial differential equations.