"Solving Matrix Inequalities whose Unknowns are Matrices"
Juan Camino (K.U. Leuven, PMA)
This talk presents algorithms for numerical solution
of convex matrix inequalities in which the variables
naturally appear as matrices. This includes, for
instance, many systems and control problems. To use these
algorithms, no knowledge of linear matrix inequalities
(LMIs) is required. However, as tools, they preserve many
advantages of the linear matrix inequality framework.
Our method has two components: 1) a numerical algorithm
that solves a large class of matrix optimization problems;
2) a symbolic ``Convexity Checker'' that automatically
provides a region which, if convex, guarantees that the
solution from (1) is a global optimum on that region.
The algorithms are partly numerical and partly symbolic and
since they aim at exploiting the matrix structure of the
unknowns, the symbolic part requires the development of new
computer techniques for treating noncommutative algebra.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
