Convergence under Subdivision and Complexity of Polynomial Minimization in the Simplicial Bernstein Basis
Résumé
In this article, we address the question of minimizing a real polynomial over the standard simplex. This problem can be solved with a branch-andbound method, using the Bernstein form of the polynomial. Such methods have been widely studied from a numerical point of view, and re nements have been proposed to speed up the computational time. We are here interested in the basic branch-and-bound algorithm (and its complexity), which has the advantage to lead to certi ed proofs.