Towards a new direct algorithm: a two-points based sampling method

Abstract. The DIRECT algorithm was motivated by a modification to Lip-schitzian optimization. The algorithm begins its search by sampling the ob-jective function at the midpoint of an interval, where this function attains its lowest value, and then divides this interval by trisecting it. One of its weak-ness is that if a global minimum lies at the boundaries, which can never be reached, the convergence of the algorithm will be unecessary slow. We present a one-dimensional variante of the DIRECT algorithm based on another strat-egy of sudividing the search domain. It consists of decreasing the number of intervals and increasing the number of sampling points, by interverting the roles of dividing and sampling at some steps of the DIRECT algorithm, and thus, overcoming this disadvantage. 1. Introduction. The original DIRECT ”DIviding RECTangles ” algorithm, developed by Donald. R. Jones et al. [10], was essentialy designed for finding the global minimum of a mul-tivariate function. The algorithm was motivated to overcome some of the problem