Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

A Smoothing Method with Appropriate Parameter Control Based on Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

We deal with complementarity problems over second-order cones. The complementarity problem is an important class of problems in the real world and involves many optimization problems. The complementarity problem can be reformulated as a nonsmooth system of equations. Based on the smoothed Fischer-Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system. The proposed method controls a smoothing parameter appropriately. We show the global and quadratic convergence of the method. Finally, some numerical results are given.

Effects of Clearance on Normal Mode Frequencies of a Nonsmooth System

The effects of a clearance or interference on the normal mode frequencies of a two-dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation. First, the exact bilinear natural frequencies of a single degree-of-freedom system are analytically obtained in terms of the amount of clearance and the strength of nonlinearity, and an equivalent linear system is derived. These results are in turn used to construct three methods which approximate the bilinear frequencies for the 2-dof system in which the resulting approximate frequencies are compared with those obtained from numerical simulations. The results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance/interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation.