A Proximal Analytic Center Cutting Plane Algorithm for Solving Variational Inequality Problems
نویسندگان
چکیده
Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper.
منابع مشابه
An analytic center cutting plane method for pseudomonotone variational inequalities
We consider an analytic center algorithm for solving generalized monotone variational inequalities in R", which adapts a recent result due to Goffin et al. (1993) to the numerical resolution of continuous pseudomonotone variational inequalities.
متن کاملHomogeneous Analytic Center Cutting Plane Methods for Convex Problems and Variational Inequalities
In this paper we consider a new analytic center cutting plane method in a projective space. We prove the eeciency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained minimization. Our analysis is valid even for the problems whose solution belongs to the boundary of th...
متن کاملSolving variational inequalities with a quadratic cut method: a primal-dual, Jacobian-free approach
We extend in two directions the Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), introduced by Denault and Go.n in 1998. First, we de9ne a primal–dual method to 9nd the analytic center at each iteration. Second, the Broyden–Fletcher–Goldfarb– Shanno Jacobian approximation, of quasi-Newton fame, is used in the de9nition of the cuts...
متن کاملA Cutting Plane Method for Solving Quasimonotone Variational Inequalities
We present an iterative algorithm for solving variational inequalities under the weakest monotonicity condition proposed so far. The method relies on a new cutting plane and on analytic centers.
متن کاملOn a Primal-Dual Analytic Center Cutting Plane Method for Variational Inequalities
We present an algorithm for variational inequalities V I(F , Y ) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mappingF is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. Linear equalities that may be included in the defin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012