About the project
This PhD project uses ideas from pure mathematics to create faster and more reliable optimization algorithms for machine learning, engineering and data science. It is especially suited to mathematically trained students who want to move into computational research, even with little programming experience.
The PhD project explores how ideas from pure mathematics can be drawn upon to improve the design, analysis, abstraction and computational efficiency of mathematical optimization algorithms arising in applied mathematics, machine learning and engineering.
The specific mathematical direction is flexible and will be shaped by the student’s background and interests. Possible directions include variational analysis and nonsmooth optimization; functional analysis and monotone operator methods; stochastic analysis for uncertainty-aware optimization; PDE techniques for constrained optimization; harmonic analysis for signal and inverse problems; convex and algebraic geometry for optimization and control; discrete topology for graph-based information retrieval; and persistent homology or topological data analysis.
The central emphasis is computational rather than purely theoretical. Pure mathematics is used as a source of structure, abstraction and analytical tools that can lead to faster algorithms, stronger convergence guarantees, improved numerical stability, dimensional reduction, or more efficient representations of optimization problems. The aim is to translate mathematical structure into concrete computational advantage.
This project is suited to students with training in pure mathematics who wish to transition towards applied or computational mathematics related to optimization or machine learning. Prior programming experience is not essential; limited coding experience is acceptable. A strong mathematical background, mathematical maturity, and willingness to engage with computational problems are more important.
The School of Engineering is committed to promoting equality, diversity inclusivity as demonstrated by our Athena SWAN award. We welcome all applicants regardless of their gender, ethnicity, disability, sexual orientation or age, and will give full consideration to applicants seeking flexible working patterns and those who have taken a career break. The University has a generous maternity policy, onsite childcare facilities, and offers a range of benefits to help ensure employees’ well-being and work-life balance. The University of Southampton is committed to sustainability and has been awarded the Platinum EcoAward.
