191 research outputs found
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
A Probability-one Homotopy Algoithm for Non-Smooth Equations and Mixed Complementarity Problems
A probability-one homotopy algorithm for solving nonsmooth equations is described. This algorithm is able to solve problems involving highly nonlinear equations,where the norm of the residual has non-global local minima.The algorithm is based on constructing homotopy mappings that are smooth in the interior of their domains.The algorithm is specialized to solve mixed complementarity problems through the use of MCP functions and associated smoothers.This specialized algorithm includes an option to ensure that all iterates remain feasible.Easily satisfiable sufficient conditions are given to ensure that the homotopy zero curve remains feasible,and global convergence properties for the MCP algorithm are developed.Computational results on the MCPLIB test library demonstrate the effectiveness of the algorithm
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
The convergence of a one-step smoothing Newton method for P0-NCP based on a new smoothing NCP-function
AbstractThe nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the solution of a nonsmooth system of equations. By introducing a new smoothing NCP-function, the problem is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is proposed for solving the nonlinear complementarity problem with P0-function (P0-NCP) based on the new smoothing NCP-function. The proposed algorithm solves only one linear system of equations and performs only one line search per iteration. Without requiring strict complementarity assumption at the P0-NCP solution, the proposed algorithm is proved to be convergent globally and superlinearly under suitable assumptions. Furthermore, the algorithm has local quadratic convergence under mild conditions
A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
10.1137/S1052623400379620SIAM Journal on Optimization143783-80
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