Advanced Nonlinear Optimisation

Many optimisation problems in the real world are inherently nonlinear. A variety of industries, including telecommunications networks, underground mining, microchip design, computer vision, facility location and supply chain management, depend on the efficient solution of nonlinear programs. This subject introduces the foundational mathematical concepts behind nonlinear optimisation. Some of the concepts covered include convex analysis, optimality conditions, conic programming, and duality. Various methods to solve nonlinear programs are covered, including iterative methods such as conjugate gradient methods, barrier methods and subgradient methods. This subject also explores the application of geometric methods such as perturbation and variational approaches to problems in facility location and network design.