My research on the theory and implementation of Interior Point Methods for linear and quadratic programming concentrated particularly on the study of search directions and warm-start approaches.
During my PhD, under the supervision of Jacek Gondzio, I have improved the implementation of corrector directions in the HOPDM interior point solver (COAP 2008), before moving to work with the structure-exploiting parallel solver OOPS. I have implemented an SMPS interface for OOPS, HOPDM and CPLEX (extended to LP_SOLVE and GLPK), which allows to solve a stochastic programming problem by formulating the corresponding deterministic equivalent problem. This implementation allows to solve a problem instance with warm-start, by first solving a problem with reduced dimensions (Mathematical Programming 2011).
I have been employed on an EPSRC funded project with Andreas Grothey, in which we continued the investigation of warm-start strategies for interior point methods in the context of stochastic programming.
This led to consider a multi-step approach, in which the number of intermediate problems can be more than one (ERGO 09-007), and a decomposition-like strategy, in which we generate and warm-start the subproblems rooted at the second-stage nodes (COAP 2013). I also designed the stochastic programming extension for the structure-conveying modelling language SML (Mathematical Programming Computation 2009).
Bioinformatics and machine learning
In October 2009 I moved to the Centre for Population Health Sciences, working on the genetic epidemiology software admixmap with Paul McKeigue: I extended it to work correctly on the X chromosome and we used this to better understand the genetic determinants of sarcoidosis in Afro-American populations (Genes and Immunity 2011). Afterwards, I implemented a computationally efficient factorization that allows to exploit pedigree data in hours rather than in weeks (Genetic Epidemiology 2013).
Since March 2012 I've been working on the SUMMIT project, a European research consortium dedicated to diabetes complications. I'm a member of Work Package 2 (non-genetic biomarkers) and Work Package 5 (data mining and in-silico modelling). In this context, we apply and develop machine learning algorithms to biomarker screening and prediction from high-dimensional data. As complications, we principally looked at cardiovascular disease (Diabetologia 2015) and rapid progression of diabetic chronic kidney disease (Kidney International 2015).