Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules

Several variations of index selection rules for simplex type algorithms for linear programming, like the Last-In-First-Out or the Most-Often-Selected-Variable are rules not only theoretically finite, but also provide significant flexibility in choosing a pivot element. Based on an implementation of the primal simplex and the monotonic build-up (MBU) simplex method, the practical benefit of the … Read more

The s-Monotone Index Selection Rule for Criss-Cross Algorithms of Linear Complementarity Problems

In this paper we introduce the s-monotone index selection rules for the well-known crisscross method for solving the linear complementarity problem (LCP). Most LCP solution methods require a priori information about the properties of the input matrix. One of the most general matrix properties often required for finiteness of the pivot algorithms (or polynomial complexity … Read more