MTH5331 · Nonlinear optimisation

Overview

This unit introduces the theory of nonlinear optimisation, along with numerical methods for solving both unconstrained and constrained problems, and the mathematical foundations that explain their behaviour and convergence. Topics include convexity, necessary and sufficient optimality conditions, gradient descent, Newton’s method and its variants (globalised, inexact, and quasi-Newton), trust-region methods, projected gradient descent, Newton–Lagrange iteration, penalty methods, and sequential quadratic programming (SQP). A small practical component focuses on applying nonlinear optimisation techniques to problem-solving, with an emphasis on understanding and formulation rather than implementation

Areas of study: Master of Mathematics

Offerings

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

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. Select and apply numerical methods for nonlinear optimisation problems in a real-world context;
5. Communicate concepts and arguments related to nonlinear optimisation.

Workload

• One 2-hour applied class (in weeks 2, 4, 6, 8, 10, 12); • Two 1.5 -hour seminars and • Eight hours of independent study per week.

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