Synopsis for C12.1b: Continuous Optimization

Level: M-level Method of Assessment: Written examination. Weight: Half-Unit (OSS paper code 2B88).

Overview

Optimization deals with the problem of minimising or maximising a mathematical model of an objective function such as cost, fuel consumption etc. under a set of side constraints on the domain of definition of this function. Optimization theory is the study of the mathematical properties of optimization problems and the analysis of algorithms for their solution. The aim of this course is to provide an introduction to nonlinear continuous optimization specifically tailored to the background of mathematics students.

Synopsis

Part 1: Unconstrained Optimization
Optimality conditions, Newton's method for nonlinear systems, Convergence rates, Steepest descent method, General line search methods (alternative search directions, e.g. Newton, CG, BFG, ...), Trust region methods, Inexact evaluation of linear systems, iterative methods and the role of preconditioners.

Part 2: Constrained Optimization
Optimality/KKT conditions, Lagrange Multipliers, Penalty methods and SQP for equality constrained optimization, Interior penalty / barrier methods for inequality constrained optimization.

Lecture notes will be made available for downloading from the course webpage.
To complement the notes, reading assignments will be given from the book of J.Nocedal and S.J.Wright, Numerical Optimisation, (Springer, 1999).