The aim of this module is to equip you with the tools to formulate and solve general constrained and unconstrained optimisation problems. The module covers several introductory topics in optimisation such as necessary and sufficient conditions of optimality, basic optimization algorithms (gradient, Newton, conjugate directions, quasi-Newton), Kuhn-Tucker conditions, penalty method, recursive quadratic programming, and global optimization. Each topic is covered in a mathematical rigorous way with attention to regularity, convergence conditions, and complexity. The module assumes prior basic calculus and linear algebra knowledge such as multivariable calculus, sequences, compactness, and eigenvalues.

Upon successful completion of this module, you will be able to: Formulate simple unconstrained and constrained optimization problems Classify optimal solutions Apply the correct methods to solve such problems Write basic unconstrained optimization algorithms and assess their convergence and numerical properties Apply the notion of penalty in the solution of constrained optimization problems Change constrained optimization problems into equivalent unconstrained problems Apply basic algorithms for the solutions of global optimization problems

Necessary and sufficient conditions of optimality Line search The gradient method, Newton's method, conjugate direction methods, quasi-Newton methods, methods without derivatives Kuhn-Tucker conditions Penalty function methods Exact methods Recursive quadratic programming Global optimization