A new simple homotopy algorithm for linear programming I

Abstract

We present λ new homotopy algorithm for linear programming. Its salient features are its simple description, and that it arises naturally from mathematical considerations. Specifically, the algorithm is defined by λ homotopy between the singular piecewise linear system (representing the given problem to be solved) and a nonsingular linear system (incorporating all the problem data). In contrast to many homotopy algorithms whose starting points are independent of the particular problem (such as the Dantzig-Lemke Simplex algorithm), this algorithm utilizes all relevant data to start. While the algorithm is primarily of theoretical interest, preliminary computer experiments suggest orthant counts typically favorable to Lemke pivots on large problems.