The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to th...

The paper generalizes the Mangasarian-Ren 10] error bounds for linear complementarity problems (LCPs) to nonlinear complementarity problems (NCPs). This is done by extending the concept of R 0-matrix to several R 0-type functions, which include a subset of monotone functions as a special case. Both local and global error bounds are obtained for the R 0-type and some monotone NCPs.

Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a ...

We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algori...

In this report an iterative method from the theory of maximal monotone operators is transfered into the context of linear complementarity problems and numerical tests are performed on contact problems from the field of rigid multibody dynamics.

We consider the stochastic linear complementarity problem (SLCP) involving a random matrix whose expectation matrix is positive semi-definite. We show that the expected residual minimization (ERM) formulation of this problem has a nonempty and bounded solution set if the expected value (EV) formulation, which reduces to the LCP with the positive semi-definite expectation matrix, has a nonempty ...

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation|one that has fewer constraints than the \standard" QP formulation|is available. We mention several instances of this class, including the known case in which the coe cient matrix in the LCP ...

We introduce a Cartesian P -property for linear transformations between the space of symmetric matrices and present its applications to the semidefinite linear complementarity problem (SDLCP). With this Cartesian P -property, we show that the SDLCP has GUS-property (i.e., globally unique solvability), and the solution map of the SDLCP is locally Lipschitzian with respect to input data. Our Cart...

Two corrector-predictor interior point algorithms are proposed for solving monotone linear complementarity problems. The algorithms produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm can be im...

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natura...