Introduction to Optimisation

AIMS

This subject provides a rigorous introduction to the mathematics of optimisation, as used across all of science and particularly in engineering design. There is an emphasis on both the theory and application of optimisation techniques, with a focus on fundamental areas such as nonlinear programming. This subject is intended for research higher-degree students in engineering.

REFERENCE TEXTS

• Numerical Optimization, Nocedal and Wright
• Nonlinear Programming, Bertsekas
• Convex Optimization Algorithms, Bertsekas

LECTURE SLIDES

• Preliminaries and Introduction
• Line Search
• Quasi-Newton Methods (BFGS)
• Convexity
• Least-squares Problems
• Derivative Free Optimisation
• Theory of Constrained Optimisation
• Duality, Subgradient Methods, and Dual Decomposition
• Gradient Projection
• Penalty and Augmented Lagrangian Methods
• Interior Point Methods
• Application – Learning
• Application – Other Engineering

Lecture videos can be found here.