Tibor Illés 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
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
Linear Complementarity Problems ($LCP$s) belong to the class of $\mathbb{NP}$-complete problems. Therefore we can not expect a polynomial time solution method for $LCP$s without requiring some special property of the matrix coefficient matrix. Our aim is to construct some interior point algorithms which, according to the duality theorem in EP form, gives a solution of … Read more
The linear complementarity problem (LCP) belongs to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient, moreover in … 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 analyze a version of the Mizuno-Todd-Ye predictor-corrector interior point algorithm for the P_*(\kappa)-matrix linear complementarity problem (LCP). We assume the existence of a strictly positive feasible solution. Our version of the Mizuno-Todd-Ye predictor-corrector algorithm is a generalization of Potra’s (2002) conclusions on the LCP with P_*(\kappa)-matrices. To derive a formulation of the complexity for … Read more
Sufficient optimality criteria for linearly constrained, concave minimization problems is given in this paper. Our optimality criteria is based on the sensitivity analysis of the relaxed linear programming problem. Our main result is similar to that of Phillips and Rosen (1993), however our proofs are simpler and constructive. Phillips and Rosen (1993) in their paper … 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