The paper establishes a computational encIosure of the solution of the linear complementarity problem (q, M), where M is assumed to be an H-matrix with a positive main diagonal. A dass of problems with interval data, which can arise in approximating the solutions of free boundary problems, is also treated successfully.

ABSTRACT We propose a modified penalty embedding for solving complementarity problem (LCP). This embedding is a special one parametric optimization problem P(t), t∈[0,1]. Under the condition (A3) (a modified Enlarged Mangasarian Fromovitz Constrait Qualification), (A4) (P(t) is JongenJonker -Twilt regular) and two technical assumptions (A1) and (A2) there exists a path in the set of stationary ...

The linear complementarity problem (LCP ) belongs to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCP s 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 this case all feasible solutions are complementary. Furthermore...

The non-linear complementarity problem NLCP is to find a vector z in IR satisfying 0 6 z ⊥ f(z) > 0, where f is a given function. This problem can be solved by several methods but the most of these methods require a lot of arithmetic operations, and therefore, it is too difficult, time consuming, or expensive to find an approximate solution of the exact solution. In this paper we give a new met...

T paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons ar...

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has O((1+ κ)√nL)-iteration complexity, the same as Miao’s method, but our error est...

Linear Complementarity Problems (LCPs) belong 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 coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, ...

Although the general linear complementarity problem (LCP) is NP-complete, there are special classes that can be solved in polynomial time. One example is the type where the defining matrix is nondegenerate and for which the n-step property holds. In this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n-step vector and matrix. It i...

In a recent paper, J. K. Aitchison and N. K. Upton have proposed a mathematical model of the behaviour of a cloud formed immediately after the sudden release of a pollutant, together with an algorithm for determining numerical solutions of the resulting system of constrained nonlinear equations and complementarity relations. This algorithm requires, at each step, the solution of a special Linea...

We present a modified version of the infeasible-interiorpoint algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545–561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which targets at the μ-center. It results a better iteration bound.