Handbook

This is an advanced level course in optimization for undergraduate students from all disciplines. Optimization is a field that develops techniques for finding the best possible choice from numerous available alternatives for a given criterion. It provides mathematical methods and numerical algorithms for solving decision-making problems in industry, commerce and scientific disciplines. Optimization methods are likely to have significant impact in many application areas of optimization, such as inventory management, energy distribution and medical treatment planning, by improving inventory controls or reducing the distribution costs or increasing the efficacy of medical treatments. Topics covered in this course include optimization modelling; convexity of sets and functions; unconstrained and constrained optimization problems; optimality and duality principles; numerical methods such as Newton, conjugate gradient and penalty methods; optimal control problems; differential equations; the Pontryagin Maximum Principle; autonomous control problems with fixed and free targets. This is a mathematics course using linear algebra, multi-variable calculus and differential equation techniques.