2022 Doctoral Award Winner
Dr Spyridon Pougkakiotis - University of Dundee
The thesis of Spyridon Pougkakiotis is in the general area of numerical optimisation and focuses on interior point methods for solving linear, convex quadratic and semi-definite programming problems. This is an important area of research because many practical applications require multiple convex optimisation problems to be solved as subproblems.
Convex optimisation problems are often solved by interior point methods that utilise barrier functions when there are inequality constraints. However, unless certain conditions are satisfied, these methods may fail to deliver a solution of the problem either due to numerical instability or due to the large size of the subproblems that need to be solved. A technique known as regularisation is commonly used to improve the reliability of interior point methods.
However, previous studies have neither produced a thorough theoretical analysis nor a systematic method of tuning the parameters used in regularisation. The thesis resolves these issues by establishing cases that exhibit polynomial complexity of applying interior point methods with regularisation and by introducing effective strategies for tuning the parameters used in regularisation. The practical benefits of regularisation are demonstrated on real-life problems arising is several application areas such as portfolio optimisation, machine learning and medical imaging.
The external examiner of Spyridon Pougkakiotis comments about being very impressed by “the quality of his academic writing and his contributions to the field of numerical optimization”. The supervisor states that Spyridon Pougkakiotis is by far the most talented PhD student he has supervised and expects him become a future leader in the world of research. The main findings of the thesis have been published as seven papers in high-quality journals.
These papers have received a total of 37 citations, which is a remarkably high considering that only 18 months have elapsed since the PhD viva.