Interior dual proximal point algorithm for linear programs

Abstract

A new algorithm for solving a linear program based on an interior point method applied to the dual of a proximal point formulation of the linear program is presented. This dual formulation contains only the nonnegativity constraint on some of the variables. This simple constraint allows us to start the algorithm without a Phase 1 method required by many other variants of the interior point method. Numerical results from a large set of test problems show that the proposed algorithm can be very competitive with other interior point methods and with MINOS 5.3, a state-of-the-art linear programming package based on the simplex method. Global convergence of the algorithm is also established. © 1994.