An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...

In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...

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...

This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to co...

We consider the Fold Complementarity Problem, which is one of the recent subjects in complementarity theory. It is a mathematical model used in economics in the study of distributive problems (cf. [25], [5]). A particular case is the k-Fold Complementarity Problem, studied using a variant of the notion of Z-function by A. Villar [25]. In this way, Villar obtained the solution of this problem as...

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...