Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied

Abstract

This paper considers the primal simplex method for linearly constrained convex quadratic programming problems. Finiteness of the algorithm is proven when s-monotone index selection rules are applied. The proof is rather general: it shows that any index selection rule that only relies on the sign structure of the reduced costs / transformed right hand side vector and for which the traditional primal simplex method is finite is necessarily finite as well for the primal simplex method for linearly constrained convex quadratic programming problems.