Optimization in Finance and Energy module (MA52004)

In Finance and Energy you often want to maximise profit or minimise costs. There are usually constraints from the operational side of the business that must be adhered to. This gives rise to what is known in mathematics as a constrained optimisation problem.

In this module, you'll study optimisation methods.

Examples of these are linear and quadratic programming to solve these problems. You will learn how to apply these methods to financial portfolios and energy systems.

Throughout the module, you’ll solve practical optimisation problems. You will 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. This course equips you with tools to tackle complex problems and make impactful decisions.

What you will learn

In this module, you will:

• learn techniques for optimisation. These include:
  • 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 which can help you to 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. You will learn to do this in ways that can then be solved by mathematical techniques

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

• explain theoretical fundaments of unconstrained and constrained optimisation. This will be regarding optimality conditions and the convergence of methods
• solve optimization problems
• formulate optimization problems in finance and energy systems

Assignments / assessment

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

Teaching methods / timetable

• 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
• one hour of tutorial weekly
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturers and peers