A survey of search directions in interior point methods for linear programming

A basic characteristic of an interior point algorithm for linear programming is the search direction. Many papers on interior point algorithms only give an implicit description of the search direction. This report derives explicit expressions for the search directions used in many well-known algorithms. Comparing these explicit expressions gives a good insight into the similarities and differences between the various algorithms. Moreover, it gives a survey of projected gradient and Newton directions for all potential and barrier functions. This is done both for the affine and projective variants.