  Lens designers routinely use optimization in their everyday practice. Local
optimization algorithms lead to the nearest minimum. In this paper, a new
deterministic approach for multi-extremum optimization is proposed. Optimal
solutions for even moderate complexity optical architectures are shown to be
located within extended merit function valleys. Merit function minimums are
separated by saddle points. An effective algorithm to travel over these valleys
from one local minimum through a saddle point to another minimum is proposed.
From this new minimum, a new valley is found which leads through another saddle
point to another minimum and so on.. In a finite number of steps, a complete
mutually connected system of stationary points (minimums and saddle points) are
revealed, giving a reasonable assurance that the search is completed.
