In this paper, we present a new path-following interior-point algorithm for -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, , which is as good as the linear analogue.

We consider an extension of the horizontal linear complementarityproblem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the bilinear objective function under a monotonicity assumption, the polyhedrality of the solution set of a ...

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...

We deene a minimization problem with simple bounds associated to the horizontal linear complementarity problem (HLCP). When the HLCP is solvable, its solutions are the global minimizers of the associated problem. When the HLCP is feasible, we are able to prove a number of properties of the stationary points of the associated problem. In many cases, the stationary points are solutions of the HLC...

We consider the extended linear complementarity problem (XLCP) introduced by Mangasarian and Pang [22], of which the horizontal and vertical linear complementarity problems are two special cases. We give some new sufficient conditions for every stationary point of the natural bilinear program associated with XLCP to be a solution of XLCP. We further propose some unconstrained and bound constrai...

we present an improved version of a full nesterov-todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (bull. iranian math. soc.,40(3), 541-564, (2014)). in the earlier version, each iteration consistedof one so-called feasibility step and a few -at most three -centering steps. here, each iteration consists of only a feasibilitystep. thus, the new alg...

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...