A note on a potential reduction algorithm for LP with simultaneous primal-dual updating

Potential function reduction algorithms for linear programming and the linear complementarity problem use key projections and which are derived from the ‘double’ potential function, , where x and s are primal and dual slacks vectors. For non-symmetric LP duality the authors show that the existence of satisfying such that and yields simultaneous primal and dual projection-based updating during the process of reducing the potential function . The role of in an simultaneous primal-dual update algorithm is discussed.