17,827 research outputs found
An extended Gauss-Seidel method for a class of multi-valued complementarity problems
The complementarity problem is one of the basic topics in nonlinear analysis; however, the methods for solving complementarity problems are usually developed for problems with single-valued mappings. In this paper we examine a class of complementarity problems with multi-valued mappings and propose an extension of the Gauss-Seidel algorithm for finding its solution. Its convergence is proved under off-diagonal antitonicity assumptions. Applications to Walrasian type equilibrium problems and to nonlinear input-output problems are also given. © 2008 Springer-Verlag
A Semismooth Newton Method for Tensor Eigenvalue Complementarity Problem
In this paper, we consider the tensor eigenvalue complementarity problem
which is closely related to the optimality conditions for polynomial
optimization, as well as a class of differential inclusions with nonconvex
processes. By introducing an NCP-function, we reformulate the tensor eigenvalue
complementarity problem as a system of nonlinear equations. We show that this
function is strongly semismooth but not differentiable, in which case the
classical smoothing methods cannot apply. Furthermore, we propose a damped
semismooth Newton method for tensor eigenvalue complementarity problem. A new
procedure to evaluate an element of the generalized Jocobian is given, which
turns out to be an element of the B-subdifferential under mild assumptions. As
a result, the convergence of the damped semismooth Newton method is guaranteed
by existing results. The numerical experiments also show that our method is
efficient and promising
Hybrid Newton-type method for a class of semismooth equations
In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem
- …