In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient. Keywords—Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Err...

In this paper, we present a new path-following interior-point algorithm for *( ) P κ -horizontal linear complementarity problems (HLCPs). The algorithm uses only full-Newton steps which has the advantage that no line searchs are needed. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, (1 ) log n O n κ ε   +     , which is as ...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to “right-hand-side perturbations” of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability or condi...

In this paper we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problem (HLCP). This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by suitable perturbation in HLCP problem. Then, we use so-called feasibility steps that serves to generate strictly feasible iterates for the ...