Novel global optimization algorithms: binary construction and the saddle-point method

This paper describes our experience with global lens optimization using algorithms that can modify an existing lens construction in an optimal way or create an entirely new construction. The binary-search method assembles lens elements according to the bits in a binary number, ensuring that all combinations of power are tested, while the saddle-point method can either add elements to a starting lens or start from scratch. The latter algorithm also naturally leads to a method of removing an element in an optimum way, which can sometimes simplify a lens with no loss of quality.