DIRECT algorithm: A new definition of potentially optimal hyperrectangles

We propose a new version of potentially optimal intervals for the DIRECT algorithm. A two-points based sampling method is presented. The method starts from a distingished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval is obtained by translating the initial interval towards the lowest function value : min{f(ci),f(ci+1)} and then overcoming the disadvantage if the global minimum lies at the boundaries. Two-dimensional version of our subdivision and sampling method is also discussed.