The s-monotone index selection rules for pivot algorithms of linear programming

In this paper we introduce the concept of s-monotone index selection rule for linear programming problems. We show that several known anticycling pivot rules like the minimal index-, last-in-first-outand themost-often-selected-variable pivot rules are s-monotone index selection rules. Furthermore, we show a possible way to define new s-monotone pivot rules. We prove that several known algorithms like the primal (dual) simplexand MBU-simplex algorithms and criss-cross algorithm with s-monotone pivot rules are finite methods. Therefore, one possible research direction in the area of pivot algorithms might be to find smonotone index selection rules that have interesting properties either from theoretical or from computational (for example larger flexibility in pivot selection) viewpoint.