Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)

The problem of approximately factoring a real or complex multivariate polynomial f seeks minimal perturbations ? f to the coefficients of the input polynomial f so that the deformed polynomial f +Δ f has the desired factorization properties. Effcient algorithms exist that compute the nearest real or complex polynomial that has non-trivial factors (see [3,6 ]and the literature cited there). Here we consider the solution of the arising optimization problems polynomial optimization (POP)via semide finite programming (SDP). We restrict to real coe cients in the input and output polynomials.