A parallel-computing solution for optimization of polynomials

In this paper, we consider optimization of polynomials in a parallel computing environment. Algorithms for optimization of polynomials can be used to solve NP-hard control problems such as stability of nonlinear and delayed systems. Unfortunately, the high computational costs of current algorithms such as sum-of-squares has limited its use to relatively small problems. In this paper we review several results on polynomial representation which and show that these results can be used to develop an algorithm for polynomial optimization with a naturally parallel structure. In particular, we design and implement a massively parallel algorithm in MPI which tests positivity of polynomials. Test results confirm that the implementation has high efficiency with relatively low overhead.