Efficiency and implementation of simplicial zero point algorithms

In this paper we compare the efficiency of several simplicial variable dimension algorithms. To do so, we first treat the issues of degeneracy and accelerating. We present a device for solving degeneracy. Furthermore we compare several accelerating techniques. The technique of iterated quasi-Newton steps after each major cycle of the simplicial algorithm is implemented in a computer code, which is used to compare the efficiency of the (n+1)-ray, 2n-ray, 2 ⁿ -ray and (3 ⁿ −1)-ray algorithms. Except for the (n+1)-ray algorithm, the number of function evaluations does not differ very much between the various algorithms. It appeared, however, that the 2 ⁿ -algorithm needs considerably less computation time.