Deciding positivity of multisymmetric polynomials

摘要: The question how to certify non-negativity of a polynomial function lies at the heart Real Algebra and also has important applications Optimization. In this article we investigate in context multisymmetric polynomials. setting generalize characterization non-negative symmetric polynomials given Timofte (2003), Riener (2012) by adapting method proof developed (2013). One particular case where our results can be applied is certifying that (multi-)symmetric defines convex function. As direct corollary main result deduce fixed degree it possible derive test for convexity which makes use special structure follows are able drastically simplify algorithmic complexity presence symmetry. This not expected general (i.e. non-symmetric) case, known testing NP-hard already 4 (Ahmadi et al., 2013).