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Lens designers routinely use optimization in their everyday practice. Localoptimization algorithms lead to the nearest minimum. In this paper, a newdeterministic approach for multi-extremum optimization is proposed. Optimalsolutions for even moderate complexity optical architectures are shown to belocated within extended merit function valleys. Merit function minimums areseparated by saddle points. An effective algorithm to travel over these valleysfrom 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 saddlepoint to another minimum and so on.. In a finite number of steps, a completemutually connected system of stationary points (minimums and saddle points) arerevealed, giving a reasonable assurance that the search is completed.

Multi-extremum optimization in lens design: navigation through merit function valleys maze