M/E23

Spectrahedra are sets of the form fx 2 Rn j Ik + L1x1 + ...Lnxn is pos. semidefiniteg, where k 2 N and Li are hermitian k  k-matrices. They are a generalization of polyhedra and useful for polynomial optimization problems (semidefinite programming). Given a spectrahedron S, we want to analyze the question which tuples L = (L1, ..., Ln) define S and if there is a ``smallest`` description of S. In order to give a positive answer, we equip the input argument S with more structure by making it a so-called free spectrahedron.

Dr. Tom-Lukas Kriel

Universität Konstanz