We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity p...

Recently, Tseng extended several merit functions for the nonlinear complementarity problem to the semide nite complementarity problem (SDCP) and investigated various properties of those functions. In this paper, we propose a new merit function for the SDCP based on the squared Fischer-Burmeister function and show that it has some favorable properties. Particularly, we give conditions under whic...

A non-interior continuation method is proposed for nonlinear complementarity problems. The method improves the non-interior continuation methods recently studied by Burke and Xu 1] and Xu 29]. Our deenition of neighborhood for the central path is simpler and more natural. In addition, our continuation method is based on a broader class of smooth functions introduced by Chen and Mangasarian 7]. ...

In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known method...

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...

This paper proposes a validation method for solutions of linear complementarity problems. The validation procedure consists of two sufficient conditions that can be tested on a digital computer. If the first condition is satisfied then a given multidimensional interval centered at an approximate solution of the problem is guaranteed to contain an exact solution. If the second condition is satis...

Recently, Tseng extended several merit functions for the nonlinear complementarity problem to the semide nite complementarity problem (SDCP) and investigated various properties of those functions. In this paper, we propose a new merit function for the SDCP based on the squared Fischer-Burmeister function and show that it has some favorable properties. Particularly, we give conditions under whic...

The linear complementarity problem is to find vector z in IR satisfying z (Mz + q) = 0, Mz + q > 0, z > 0, where M as a matrix and q as a vector, are given data; this problem becomes in present the subject of much important research because it arises in many areas and it includes important fields, we cite for example the linear and nonlinear programming, the convex quadratic programming and the...

We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCP-function-based reformulations of infinite-dimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our results generalize semismoothness and -order semismoothness from finite-dimensional spaces to a Banach...