MATH 271 ABC: NUMERICAL OPTIMIZATION

Winter 2012


Numerical optimization problems arise in many applications, ranging from the optimal control of the Mars Lander, to the optimal design of the hull of the New Zealand entry to the Americas Cup yacht race. Numerical optimization may be briefly described as the formulation and analysis of algorithms for the minimization or maximization of a nonlinear function subject to nonlinear constraints on the variables.

This class is intended as an introduction to the design and analysis of algorithms for numerical optimization. It is suitable for graduate students in the applied and natural sciences who want to develop an understanding of practical methods for optimization. If time permits, discussion will include some case studies involving real problems.

Specific topics will include the solution of nonlinear equations; Newton and quasi-Newton methods; optimality conditions; the Karush-Kuhn-Tucker conditions; linear, quadratic programming and nonlinear programming; convex programming; penalty- and barrier-function methods; interior-point methods; KKT systems and their numerical solution; augmented Lagrangian methods, sequential quadratic programming (SQP) methods.

Lecture notes are available to registered students from the Class Web-Site (see below). Many homework assignments will require the use of the interactive matrix package Matlab, although no prior knowledge of Matlab is assumed. Matlab enables the student to concentrate on the fundamental ideas of numerical optimization without becoming distracted by the rigors of mental arithmetic. (``It is unworthy of excellent men to lose hours like slaves in the labour of calculation.''---Leibniz.)

Optimization humor (pdf) (thanks to Michael Saunders).

  • Lecture slides
  • ClassNotes
  • Homework
  • Homework solutions

  • Instructor: Philip E. Gill
    Time: MWF 1:00--1:50pm
    Class location: AP&M Room 2402
    Office Hours: MW 11:00am--12:00pm, AP&M' Room 5872 (or by appointment)