Optimization of Positive Generalized Polynomials Under l^p Constraints

The problem of maximizing a non-negative generalized polynomial of degree at most $p$ on the $l_p$-sphere is shown to be equivalent to a concave one. Arguments where the maximum is attained are characterized in connection with the irreducible decomposition of the polynomial, and an application to the labelling problem is presented where these results are used to select the initial guess of a continuation method.