Karmarkar's Algorithm: Variations on a Theme

This talk will present a survey of various algorithms and ideas that have been suggested in the wake of Karmarkar's original results. The talk will begin with a review of Karmarkar's original projective-scaling method. We will continue on to the affine-scaling method of Vanderbei, Meketon and Freedman, the affine-scaling method with recentering as suggested by Barnes, the merger of Huard's method of centers with Netwon's method by Renegar, the power series approach of Bayer and Lagarias, and the primal-dual approach implemented by Adler and Monteiro. Other variations will be mentioned if time permits.