Linear updates for a single-phase projective method (Q2276876)

The paper describes an enhancement to the single-phase projective algorithm proposed by \textit{G. de Ghellinck} and \textit{J.-P. Vial} [Algoritmica 1, 425-453 (1986; Zbl 0629.90058)] for the primal linear programming problem. The linear lower-bound update that they give does not ensure convergence with nonfeasible iterates, and is therefore supplemented by a quadratic procedure. In this paper, linear updates are derived that guarantee convergence of the algorithm in a polynomial number of steps.