In this paper we study linear passive electrical circuits mixed with ideal diodes and voltage/current sources within the framework of linear complementarity systems. Linear complementarity systems form a subclass of hybrid dynamical systems and as such questions about existence and uniqueness of solution trajectories are non-trivial and will be investigated here. The nature of the behaviour is ...

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx + q) ≥ 0 can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in...

We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in [5] depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang [17], where a vast set of conclusions concerning continuous trajectories is shown for monotone complementarity problems over t...

Several new interfaces have recently been developed requiring PATH to solve a mixed complementarity problem. To overcome the necessity of maintaining a diierent version of PATH for each interface, the code was reorganized using object-oriented design techniques. At the same time, robustness issues were considered and enhancements made to the algorithm. In this paper, we document the external in...

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 the present work, we determine intervals of convergence for the various parameters involved for what is known as the Generalized Accelerated Overrelaxation iterative method for the solution of the Linear Complementarity Problem. The convergence intervals found constitute sufficient conditions for the Generalized Accelerated Overrelaxation method to converge and are better than what have been...

In this paper, we establish a significant matrix class inclusion that seems to have been overlooked in the literature of the linear complementarity problem. We show that P∗, the class of sufficient matrices, is a subclass of L. In the course of demonstrating this inclusion, we introduce other new matrix classes that forge interesting new connections between known matrix classes.

This note focuses on a viscoelastodynamic problem being subject to unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, the problem can be reduced to the pseudodifferential linear complementarity problem through Fourier analysis. We prove that this problem possesses a solution, which, is obtained as the limit of a sequence of solutions of penalized probl...

In this paper, we propose a Big-? smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory deened by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has a solution. The method has been tested on the P 0 matrix linear complementarity problem with unbou...

This report gives an overview of the linear complementarity problem, as a special case of mathematical programming with equilibrium constraints. The interior point method and two versions of Lemke’s method are reviewed, as methods for solving the linear complementarity problem. The report concludes with a description of the Stackelberg game and the bimatrix game as possible applications of math...