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