Optimization research @ NALAG

There is a strong interaction between results of linear and multilinear algebra and optimization theory and algorithms.

Several decompositions in linear and multilinear algebra can be formulated as the solution of an optimization problem. E.g., the Block Term Decomposition in multilinear algebra can be computed by different optimization techniques.
Optimization over nonnegative polynomials can be formulated as a semidefinite programming problem with low displacement rank matrices.
Optimization on manifolds is related to the fact that in many optimization problems, it is important to keep the structure that is inherent to the problem.
For PDE constrained optimization problems from structures and vibrations, model reduction methods are needed to cope with the evaluation of objective function and gradients for many different frequencies.
Bounds for parametric eigenvalue problems can be obtained by optimization. It is useful for example to determine the lovasz number of a graph.

In this context the research group also participates in the center of excellence OPTEC.