We present a generalization of a homogeneous self-dual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any \big-M" parameter or two-phase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certiicate proving infeasibility. Moreover, if the MCP is polynomiall...

In this article, we propose a new class of search directions based on kernel function to solve the monotone semidefinite linear complementarity problem by primal-dual interior point algorithm. We show that algorithm benefits from best polynomial complexity, namely $ O(\sqrt{n}(\log n)^{2}\log\dfrac{n}{\epsilon})$. The implementation showed great improvement concerning time and number iterations.

In this paper, we first give a new equivalent optimization form to nonlinear complementarity problems and then establish a damped Newton method in which penalty technique is used. The subproblems of the method are lower-dimensional linear complementarity problems. We prove that the algorithm converges globally for strongly monotone complementarity problems. Under certain conditions, the method ...

In this paper, we present two different methods in order to solve a monotone linear complementarity problem (LCP ): a simplicial method (Lemke’s method) related to the Jordan’s pivot and the interior point method based on the central path. We demonstrate that a quadratic convex program (QCP ) can be written as a (LCP ) form and, thus, be solved by means of one of these two methods. We provide n...

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 ...

In this study, we implement a variant of infeasible interior-point algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the LCP as an minimization problem. Then descent iterative method is applied to latter. The direction computed via Newton method. However, maintaining positivity iterates, novel and efficient strategy proposed. Some numerical results are r...