A dynamical annealing algorithm for global optimization based on approximate solution of the Smoluchowski equation is presented. The equations of motion in the Gaussian density approximation are interpreted as a steepest descent quench on a time dependent effective potential energy surface. A relation between the convexity condition for the effective potential surface and the size of thermal fluctuations provides a definition of the critical temperature above which the distribution is delocalized and the effective potential is smooth and convex during an annealing run. This critical temperature may be significantly less than the temperature characteristic of escape from a local energy minimum.