Optimisation in Finance and Industry module (MA32010)

In finance and energy you often want to maximise profit or minimise costs, but there are usually operational constraints that must be met. This gives rise to what is known in mathematics as a constrained optimisation problem.

In this module, you'll study optimisation methods such as linear and quadratic programming. You'll learn how to apply them to financial portfolios and energy systems.

Throughout the module, you’ll solve practical optimisation problems and gain skills in modelling and computational methods. By the end, you’ll understand how optimisation underpins smarter, more effective systems in finance and energy. This will prepare you for challenges in industries where efficiency and strategy are paramount. You'll have the tools and confidence to tackle complex problems and make impactful decisions.

What you will learn

In this module, you will:

• Learn techniques for optimisation, including:
  • optimality conditions
  • line search and descent methods
  • conjugate gradient method
  • Newton's method
  • quasi-Newton methods
  • sums of squares problems
  • systems of nonlinear equations
• Be introduced to the theory of optimisation to help you choose a suitable method and know if you have found an optimal solution
• Learn to formulate different kinds of optimisation problems that arise in finance and energy, in ways that can then be solved by mathematical techniques

By the end of this module, you will be able to:

• Explain the theoretical fundamentals of unconstrained and constrained optimisation, including optimality conditions and the convergence of methods
• Solve optimisation problems
• Formulate optimisation problems in finance and energy systems

Assignments / assessment

• Laboratory assignments (20%)
• Class tests (30%) – based on non-assessed problem sheet questions
• Report with presentation (50%)

Teaching methods / timetable

• Lectures
  • One two-hour lecture weekly
  • Key points of the week's content will be discussed
  • Lecture notes covering the full module content will be available before classes
  • In-class time will be prioritised for interactive discussion
• Tutorials
  • One hour weekly
  • Solve problems individually and in groups
  • Support with difficulties provided by lecturers and peers