  We propose a family of search directions based on primal-dual entropy in the
context of interior-point methods for linear optimization. We show that by
using entropy based search directions in the predictor step of a
predictor-corrector algorithm together with a homogeneous self-dual embedding,
we can achieve the current best iteration complexity bound for linear
optimization. Then, we focus on some wide neighborhood algorithms and show that
in our family of entropy based search directions, we can find the best search
direction and step size combination by performing a plane search at each
iteration. For this purpose, we propose a heuristic plane search algorithm as
well as an exact one. Finally, we perform computational experiments to study
the performance of entropy-based search directions in wide neighborhoods of the
central path, with and without utilizing the plane search algorithms.
