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Operational Research

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.