Theory and Computation for ODE/PDE-constrained optimization

    Term: Spring 2004
    Course: ENM 520 001
    Day/Time: Mondays & Wednesdays 1:30--3:00 PM


    George Biros email:

    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.


    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 Differential-Algebraic Equations
      Uri Ascher and Linda Petzold


    • Unconstrained Optimization
      Optimality conditions
      Newton, Quasi-Newton methods
      Least Squares and Gauss-Newton 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


    Numerical analysis, basic theory of ordinary and partial differential equations.