Nonlinear optimisation

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.