Postgraduate study

Optimization and Operational Research PhD

Awards: PhD

Funding opportunities

The work in the Operational Research and Optimization research group is in three main areas: the mathematical and computing aspects of optimization, combinatorial optimization, and energy systems.

The core technology in optimization is the solution of large sparse linear and quadratic problems, and we provide world-class expertise in the two main solution methods for these: the simplex method and the interior point method. In combinatorial optimization, we provide expertise for modelling real-world problems using integer linear programming formulations and for deriving efficient exact and heuristic algorithms to solve them.

Specialist expertise in energy includes optimization of system planning and optimization, security of supply risk analysis, and decision support for public policy. We also have interests in PDE-constrained optimization, global optimization, decomposition methods, parallel computing, industrial applications of optimization and stochastic optimization.

Specific topics which could yield PhD projects include

  • Algorithms for linear and nonlinear nonconvex smooth optimization problems.
  • Optimization methods for linear, integer linear, quadratic and nonlinear programming.
  • Decomposition methods for large-scale nonlinear nonconvex constrained optimization.
  • Bundle methods.
  • Warm starts for interior point methods.
  • Pooling problems.
  • Applications of optimization in logistics.
  • Parameter uncertainty in queueing theory and revenue management.
  • Facility location and vehicle routing.

Being part of the Operational Research and Optimization group will give you the opportunity to meet and confer with academics worldwide. You will be a member of the Edinburgh Research Group in Optimization (ERGO) which, through its regular seminar series, attracts local and international researchers interested in the development of operational research and optimization. As a group, we are currently collaborating with researchers in Denmark, the Netherlands, Canada, USA, Italy, Norway, China, France, Spain, Germany and Turkey, and are invited to give addresses and organise workshops at major optimization, OR and energy conferences.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to generous library provision for research at the leading level, including the Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across the University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have your own desk with desktop computer.

We provide all our mathematics postgraduates with access to software packages such as Maple, Matlab and Mathematica. Research students are allocated parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

English language requirements

You must demonstrate a level of English language competency at a level that will enable you to succeed in your studies, regardless of your nationality or country of residence.

English language tests

We accept the following English language qualifications at the grades specified:

  • IELTS Academic: total 6.5 with at least 6.0 in each component

  • TOEFL-iBT: total 92 with at least 20 in each section

  • PTE Academic: total 61 with at least 56 in each of the Communicative Skills scores

  • CAE and CPE: total 176 with at least 169 in each paper

  • Trinity ISE: ISE II with distinctions in all four components

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS, TOEFL, PTE Academic or Trinity ISE, in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries.

If you are not a national of a majority English speaking country, then your degree must be no more than three and a half years old at the beginning of your programme of study.*

(*Revised 8/11/2018 to provide more accurate information on English language qualifications expiry dates. Revised 22/03/2019 to provide more accurate/comprehensive information.)

Find out more about our language requirements:

Read our general information on tuition fees and studying costs:

Featured funding

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK’s governments. The type and amount of financial support you are eligible for will depend on your programme, the duration of your studies, and your residency status. (Programmes studied on a part-time intermittent basis are not eligible.)

Other funding opportunities

Search for scholarships and funding opportunities:

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD

Find out more about the general application process for postgraduate programmes:

Further information

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD