Practical optimisation
4 points * Second semester * Clayton * Prerequisites: MAT2010, MAA2011 and MAA2032 * MAT2020 recommended
Objectives On the completion of this subject students will have developed basic numerical techniques in optimisation through following basic global strategies like line search and trust region techniques, quasi-Newton methods, restricted step methods, Lagrange multiplier methods for constrained optimisation, simplex method for linear programming, penalty and barrier function methods for constrained optimisation; understand necessary and sufficient conditions for local minima; solve optimisation problems in practice on computers; understand the incompleteness of the young and rapidly developing subject; be able to evaluate critically numerical algorithms.
Synopsis Numerical techniques and applications in unconstrained and constrained optimisation. Unconstrained optimisation: conditions for local minima, ad hoc methods, Newton-like methods, conjugate direction methods. Constrained optimisation: linear programming, simplex method, degeneracy, Lagrange multipliers, first and second order conditions, general linearly constrained optimisation, nonlinear programming.
Assessment Examinations (1.5 hours): 85% * Assignments: 15%
Recommended texts
Cameron N Introduction to linear and convex programming Australian Mathematical Society Lecture Series No.1, CUP, 1985
Fletcher R Practical methods of optimization 2nd edn, Wiley, 1987
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