Scaling,shifting and weighting in interior-point methods

We examine certain questions related to the choice of scaling, shifting and weighting strategies for interior-point methods for linear programming. One theme is the desire to make trajectories to be followed by algorithms into straight lines if possible to encourage fast convergence. While interior-point methods in general follow curves, this occurrence of straight lines seems appropriate to honor George Dantzig's contributions to linear programming, since his simplex method can be seen as following either a piecewise-linear path inn-space or a straight line inm-space (the simplex interpretation).Dedicated to Professor George B. Dantzig on the occasion of his eightieth birthday.Research supported in part by NSF, AFOSR, and ONR through NSF Grant DMS-8920550.