Theory and Computation for ODE/PDEconstrained optimization
Term: Spring 2004
Course: ENM 520 001
Day/Time: Mondays & Wednesdays 1:303:00 PM
Instructor
George Biros
email:
biros@seas.upenn.edu
Class description
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.
Grading
Homeworks (80%) and final project (20%).
Students can use software of their choice;
I recommend MATLAB.
Recommended texts
None, but the following texts are recommended for nonlinear
programming and numerical methods for ODEs and PDEs.

Numerical optimization
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 DifferentialAlgebraic Equations
Uri Ascher and Linda Petzold
Topics
 Unconstrained Optimization
Optimality conditions
Newton, QuasiNewton methods
Least Squares and GaussNewton methods
Line search, Trust Region methods
 Constrained Optimization
Optimality conditions
Sequential Quadratic Programming
Reduced and full space methods
Interior point methods
 Applications
Sensitivity Analysis
Boundary and Distributed parameter control
Shape/Topology Optimization
Trajectory Optimization
Inverse problems and regularization
Prerequisites
Numerical analysis, basic theory of ordinary
and partial differential equations.