The problem of approximately factoring a real or complex multivariate polynomial $f$ seeks minimal perturbations $\Delta f$ to the coefficients of the input polynomial $f$ so that the deformed polynomial $f + \Delta f$ has the desired factorization properties. Efficient algorithms exist that compute the nearest real or complex polynomials that has non-trivial factors. (see  and  and the literature cited there). Here we consider the solution of the arising optimization problems using polynomial optimization (POP) via semidefinite programming. We restrict to real coefficients in the input and output polynomials.
Proceedings of SNC 07, London, Ontario, Canada, July 25-27, 2007, pp. 203-204