Advanced Nonlinear Optimisation (MAST90142)

Graduate courseworkPoints: 12.5Not available in 2025

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Overview

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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.

Intended learning outcomes

After completing this subject, students should be able to:

  • Demonstrate an understanding of the fundamental mathematical theory behind nonlinear optimization;
  • Model and analyse nonlinear optimisation problems;
  • Apply various methods to solve nonlinear optimisation problems, including convex, non-convex, differentiable and non-differentiable problems.

Generic skills

  • Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies
  • Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis
  • Time-management skills: the ability to meet regular deadlines while balancing competing commitments

Last updated: 4 March 2025