I contribute to the following open-source software projects.
QUINOPT (QUadratic INtegral OPTimisation) is an open-source add-on for the MATLAB optimisation modelling toolbox YALMIP, aimed at the computation of rigorous upper and lower bounds on the optimal value of optimisation problems with infinite-dimensional polynomial quadratic integral inequality constraints. Such problems commonly arise from stability analysis of linear partial differential equations using the so-called energy method (also known as L2 stability), and when bounding time-averaged properties of turbulent fluid flows using the so-called background method.
CDCS (Cone Decomposition Conic Solver) is an open-source MATLAB solver for structured semidefinite programmes. It implements a selection of first-order algorithms, all based on the alternating direction method of multipliers (ADMM), for the solution of large semidefinite programmes (SDPs) characterised by a chordal sparsity pattern, and of SDPs characterised by partial orthogonality, which typically arise from sum-of-squares optimisation problems.