We investigate the resolution of the launcher ascent trajectory problem by the so-called Hamilton- Jacobi- Bellman (HJB) approach, relying on the Dynamic Programming Principle. The method gives a global optimum and does not need any initialization procedure. Despite these advantages, this approach is seldom used, because of the difficulties of computing the solution of the HJB equation for high dimension problems. The present study shows that an efficient resolution is found. An illustration of the method is proposed on a heavy class launcher, for a typical GEO mission. This study has been performed in the frame of the CNES Launchers Research & Technology program.