Interior-point Methods for Linear Programming: a Challenge to the Simplex Method

The world of mathematical programming has seen a remarkable surge of activity following publication of Karmarkar's projective algorithm in May 1984. A review of the ensuing three years has already appeared. One year later, the authors review some of the main methods and surrounding events, and focus on references that contain computational results. Keywords: Barrier-function methods, Newton's method, Karmarkar's projective method, Problem solving. (kr).