A phase-1 approach for the generalized simplex algorithm,

A new simplex variant allowing basis deficiency has recently been proposed to attack the degeneracy [1]. As a generalization of the simplex algorithm, it uses a Phase-1 procedure, solving an auxiliary problem with piecewise-linear sums of infeasibilities as its objective. In this paper, we develop another Phase-1 approach that only introduces a single artificial variable. Unlike the former, which needs a crash procedure to supply an initial basis, the proposed Phase-1 is able to get itself started from scratch, with an artificial basis having a single column. Computational results with a set of standard test problems from NETLIB are also reported.