Math 271C: Numerical Optimization

Spring 2018

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 2000 (winning) entry to the Americas Cup yacht race. Numerical optimization may be described briefly 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, engineering, 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 unconstrained optimization; optimality conditions; Newton and quasi-Newton methods; the solution of nonlinear equations; constrained optimization; 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 link below. Some 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.)

Grading options:

I prefer not to answer technical questions by email ( n emails for me to understand your question, m emails for you to understand my answer), but students are welcome to attend my office hours or see me after class.

Class notes and homeworks:

Class location: AP&M Room 2402
Class time: MWF 12:00 - 12:50pm
Instructor: Philip E. Gill
Office hours: MW 10:30pm -- 11:30am
Office: AP&M Room 5872
TA: Fangyao Su
Office hours: TBA
Office location: AP&M' 5720