MTH4331 · Nonlinear optimisation

Overview

This unit covers the theory of nonlinear optimisation, numerical methods for solving unconstrained and constrained nonlinear optimisation problems, and the mathematical theory of why these methods work. Their behaviour is explored in programming exercises using Matlab. Topics covered include convexity, necessary and sufficient optimality conditions, gradient descent, Newton’s method, globalised Newton, inexact Newton, quasi Newton, trust-region Newton, projected gradient descent, Newton-Lagrange iteration, penalty methods, and SQP methods.

Areas of study: Master of Mathematics Master of Financial Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Demonstrate an advanced understanding of nonlinear optimisation theory at a conceptual level as well as at a granular level;
2. Demonstrate an advanced understanding of the uses of common numerical methods for solving unconstrained and constrained optimisation problems, as well as their advantages and disadvantages;
3. Apply mathematical principles and theorems to quantify how fast and in what sense these numerical methods converge;
4. Implement numerical methods for nonlinear optimisation problems in Matlab;
5. Select and apply numerical methods for nonlinear optimisation problems in a real-world context;
6. Communicate concepts and arguments related to nonlinear optimisation.

Workload

• Two 1.5 -hour seminars; • One bi-weekly 2-hour applied class (commencing in week 2) and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.