Zsolt Csizmadia It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more
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
We define a variant of Anstreicher and Terlaky’s (1994) monotonic build-up (MBU) simplex algorithm for linear feasibility problems. Under a nondegeneracy assumption weaker than the normal one, the complexity of the algorithm can be given by $m\Delta$, where $\Delta$ is a constant determined by the input data of the problem and $m$ is the number … Read more
We generalize new criss-cross type algorithms for linear complementarity problems (LCPs) given with sufficient matrices. Most LCP solvers require apriori information about the input matrix. The sufficiency of a matrix is hard to be checked (no polynomial time method is known). Our algorithm is similar to Zhang’s linear programming, and Akkeleº-Balogh-Illés’s criss-cross type algorithm for … Read more