The research of the group is focussed on mathematical optimization and covers all aspects of the development of modern optimization algorithms starting from their theoretical background (convergence and worst-case complexity analysis) through their design and implementation and, finally, their applications to solve real-life problems.
The group has broad expertise in several areas of optimization: interior point methods, simplex method, nonlinear programming algorithms, combinatorial optimization techniques, stochastic programming techniques, and first-order methods. The group interacts with academics in many countries around the world.
The main threads of group's research are:
Mathematical foundations of optimization: Research covers the convergence analysis and establishing the worst-case complexity bounds for different classes of modern optimization algorithms: steepest-descent, Newton and cubic regularized methods for nonlinear programming, interior point methods and first-order methods.
Design and implementation of optimization algorithms: Research covers the study of linear algebra techniques, the exploitation of matrix sparsity in optimization methods and the use of modern computer architectures including parallel, multi-core and GPUs. This research stream has benefitted from the foundation of the Centre for Numerical Algorithms and Intelligent Software.
Applications: The methods and software developed by the group have been applied to solve real-life problems. The group has on-going collaborations and strong links with many industrial partners.