AnySOS: An anytime algorithm for SOS programming

We introduce AnySOS, an implementation of an algorithm of Renegar for solving sum-of-squares (SOS) programs arising in control applications. Renegar's algorithm is an efficient first-order method for general semidefinite programs. One of its key features, unlike other first-order methods, is that it produces feasible iterates throughout execution. This is particularly important for sum-of-squares applications: the algorithm can be stopped anytime and still return a valid certificate/proof for the underlying system. For critical and real-time applications this can be used to trade-off accuracy and running time, without compromising safety. We demonstrate the applicability of this algorithm on some illustrative examples and show that it compares very favourably with other methods for large-scale sum-of-squares programming.