  We propose a new globalization strategy that can be used in unconstrained
optimization algorithms to support rapid convergence from remote starting
points. Our approach is based on using multiple points at each iteration to
build a representative model of the objective function. Using the new
information gathered from those multiple points, a local step is gradually
improved by updating its direction as well as its length. We give a global
convergence result and also provide parallel implementation details accompanied
with a numerical study. Our numerical study shows that the proposed algorithm
is a promising alternative as a globalization strategy.
