Optimisation comes in many shapes and many forms. In the last events, we have been discussing the following, but not limited to, the following topics:
An extension of classical analysis to support optimisation in an essentially nonsmooth setting. In other words, this branch of mathematics deals with optimisation problems where the defining constraints or objective function has jumps in their values of rates of change.
Deals with the special structure engendered to an optimisation problem within which the constraints and objective functions are geometrically rotund. This enables special analysis and efficient algorithms.
The study of optimisation problems with conic constraints where the cones have special structural properties (such as linear, semidefinite and hyperbolic programming).
Mathematical framework to study decision making problems in the presence of conflicting interests.
The study of decision making problems where decisions have to be made based on incomplete information about future events. In the former case the possible futures are associated with a probability distribution and one seeks to optimise an expectation value while in the latter information arrive over the time and one seeks to optimise in the worst case.
Dynamical systems and Optimal Control
The study of systems that evolve in time whose evolution can be influenced by the choice of input parameters, in order to optimise their performance.
Combinatorial Optimisation, Networks and Graphs
Optimisation of problems in which some or all of the variables take discrete values, or when the problem’s structure exhibits discrete characteristics. Graphs are such particular discrete structures.
Algorithm Efficiency/ Complexity theory/Polynomial Approximation
Theoretical analysis of the performance of numerical algorithms that allows to measure the efficiency of the methods – theoretical analysis of the best possible performance of any algorithm for a problem that allows to characterise the hardness of a problem – design and analysis of algorithms with performance guarantees.
Modelling and Solving Real Problems
Using optimisation models for addressing real problems and challenges for the society: the group is involved in various domains of applications like environmental management, energy and natural resources management, emergency management.