Smoothing-Nonsmooth Reformulations of Variational Inequality Problems
نویسنده
چکیده
It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsmooth equations. Various properties of the reformulated functions will be investigated and Newton-type methods will be applied to solve the reformulated systems.
منابع مشابه
Solving Variational Inequality Problems via Smoothing-Nonsmooth Reformulations
It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness. When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth e...
متن کاملSmoothing Functions and A Smoothing Newton Method for Complementarity and Variational Inequality Problems
In this paper, we discuss smoothing approximations of nonsmooth functions arising from complementarity and variational inequality problems. We present some new results which are essential in designing Newton-type methods. We introduce several new classes of smoothing functions for nonlinear complementarity problems and order complementarity problems. In particular, in the first time some comput...
متن کاملVector Optimization Problems and Generalized Vector Variational-Like Inequalities
In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector vari...
متن کاملGlobal and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f(·, εk), and the derivative of f(·, εk) at xk is used as the Newto...
متن کاملA SMOOTHING NEWTON METHOD FOR THE BOUNDARY-VALUED ODEs
In this thesis, we focus on the Nonsmooth Boundary-valued ODEs, whose right-hand functions are parameterized by algebraic variables that solve the initial-valuedproblems and the nonsmooth equations. Based on the idea of the initial value tech-niques used in traditional ODEs, a smoothing Newton method originated from theQSZ method is applied to the nonmsmooth dynamic systems. Mos...
متن کامل