This paper provides a means for comparing various computer codes for solving large scale mixed complementarity problems. We discuss inadequacies in how solvers are currently compared, and present a testing environment that addresses these inadequacies. This testing environment consists of a library of test problems, along with GAMS and MATLAB interfaces that allow these problems to be easily ac...

The strict feasibility plays an important role in the development of theory and algorithms of complementarity problems. In this paper, we establish suucient conditions to ensure the strict feasibility of a nonlinear complemen-tarity problem. Our analytical method, based on a newly introduced concept of-antifeasible sequence, can be viewed as a uniied approach in proving the existence of a stric...

We propose a new algorithm for solving smooth nonlinear equations in the case where their solutions can be singular. Compared to other techniques for computing singular solutions, a distinctive feature of our approach is that we do not employ second derivatives of the equation mapping in the algorithm and we do not assume their existence in the convergence analysis. Important examples of once b...

We design a new continuation method for the solution of nonlinear complementarity problems with uniform P−functions. Similar to interior-point methods, we try to follow the central path inexactly. In contrast to interior-point methods, however, our iterates are allowed to stay outside of the positive orthant. The method is shown to be globally and superlinearly (quadratically) convergent.

The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a path-generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length acceptance criterion and a non-monotone pathsearch are then used to choose the next iterate. The algorith...

Most known continuation methods for P0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and the properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose a new homotopy formulation for the complementarity problem based on which a new homotopy conti...

Regularization methods for the solution of nonlinear complementarity problems are standard methods for the solution of monotone complementarity problems and possess strong convergence properties. In this paper, we replace the monotonicity assumption by a P0-function condition. We show that many properties of regularization methods still hold for this larger class of problems. However, we also p...

In this paper we consider the extended semide nite linear complementarity problem (XSDLCP). We propose merit functions that can constitute minimization problems equivalent to XSDLCP and show some properties of these functions. We also consider the semide nite nonlinear complementarity problem (SDNCP) and give new su cient conditions that guarantee the existence of a solution to SDNCP.

In this paper, we study some basic properties of the monotone semide nite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive de nite matrices under certain conditions. Especially, for the monotone semide nite linear complementarity problem, the trajectory converge...

In this paper we consider a general algorithmic framework for solving nonlinear mixed complementarity problems. The main features of this framework are: (a) it is well-defined for an arbitrary mixed complementarity problem, (b) it generates only feasible iterates, (c) it has a strong global convergence theory, and (d) it is locally fast convergent under standard regularity assumptions. This fra...