PENLAB: A MATLAB solver for nonlinear semidefinite optimization

Abstract: PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon} and of a new implementation from NAG \cite{naglib}: it can solve the same classes of problems and uses the same algorithm. Unlike PENNON, PENLAB is open source and allows the user not only to solve problems but to modify various parts of the algorithm. As such, PENLAB is particularly suitable for teaching and research purposes and for testing new algorithmic ideas. In this article, after a brief presentation of the underlying algorithm, we focus on practical use of the solver, both for general problem classes and for specific practical problems.