Properties of a Class of Ncp-functions and a Related Semismooth Newton Method for Complementarity Problems
نویسندگان
چکیده
In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present an exact expression of the generalized gradient for the NCP-function. The level boundedness of the merit function is discussed. Based on these results, we investigate a semismooth Newton method and give its convergence analysis. As an application, we use this method to solve the frictionless contact problem.
منابع مشابه
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
We introduce a new, one-parametric class of NCP-functions. This class subsumes the Fischer function and reduces to the minimum function in a limiting case of the parameter. This new class of NCP-functions is used in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. We present a detailed investigation of the properties of the equation operator, of the...
متن کاملA Penalized Fischer - Burmeister Ncp - Function : Theoretical Investigation and Numerical Results 1
We introduce a new NCP-function that reformulates a nonlinear com-plementarity problem as a system of semismooth equations (x) = 0. The new NCP-function possesses all the nice properties of the Fischer-Burmeister function for local convergence. In addition, its natural merit function (x) = 1 2 (x) T (x) has all the nice features of the Kanzow-Yamashita-Fukushima merit function for global conver...
متن کاملA penalized Fischer-Burmeister NCP-function
We introduce a new NCP-function in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. This new NCP-function turns out to have stronger theoretical properties than the widely used Fischer-Burmeister function and other NCP-functions suggested previously. Moreover, numerical experience indicates that a semismooth Newton method based on this new NCP-funct...
متن کاملA regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs
We consider a regularization method for nonlinear complementarity problems with F being a P0-function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed b...
متن کاملGlobally Convergent Broyden-Like Methods for Semismooth Equations and Applications to VIP, NCP and MCP
In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complemen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011