A Note on Nonlinear Approaches to Linear Programming.

Abstract : Certain new approaches to linear programming have recently received considerable publicity because of the promise of substantial improvements in efficiency compared to the simplex method. This note briefly discusses several research directions in methods for solving linear programs using nonlinear problem transformations. In particular, we describe application of a barrier transformation to the dual, and the development of sparse least-squares methods based on the LU factorization of the least-squares matrix of its transpose. (Author)