Approximate symbolic computation problems can be formulated as constrained or unconstrained optimization problems, for example: GCD [3,8,12,13,23], factorization [5,10], and polynomial system solving [2,25,29]. We exploit the special structure of these optimization problems, and show how to design efficient and stable hybrid symbolic-numeric algorithms based on Gauss-Newton iteration, structured total least squares (STLS), semide finite programming and other numeric optimization methods.