  In this paper, we construct an algorithm for minimising piecewise smooth
functions for which derivative information is not available. The algorithm
constructs a pair of quadratic functions, one on each side of the point with
smallest known function value, and selects the intersection of these quadratics
as the next test point. This algorithm relies on the quadratic function
underestimating the true function within a specific range, which is
accomplished using a adjustment term that is modified as the algorithm
progresses.
