New Alternating Direction Method for a Class of Nonlinear Variational Inequality Problems

نویسنده

  • D. R. HAN
چکیده

The alternating direction method is an attractive method for a class of variational inequality problems if the subproblems can be solved efficiently. However, solving the subproblems exactly is expensive even when the subproblem is strongly monotone or linear. To overcome this disadvantage, this paper develops a new alternating direction method for cocoercive nonlinear variational inequality problems. To illustrate the performance of this approach, we implement it for traffic assignment problems with fixed demand and for large-scale spatial price equilibrium problems.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

متن کامل

Inexact Alternating Direction Method for Variational Inequality Problems with Linear Equality Constraints

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point x̃, and then the multiplier y is updated to get the new iterate y. In order to get x, we adopt a new descent direction which is simple comp...

متن کامل

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

متن کامل

Finite Element Appoximation and Iterative Solution of a Class of Mildly Non - Linear Elliptic Equations

We describe in this report the numerical analysis of a particular class of nonlinear Dirichlet problems. We consider an equivalent variational inequality formulation on which the problems of existence, uniqueness and approximation are easier to discuss. We prove in particular the convergence of an approximation by piecewise linear finite elements. Finally, we describe and compare several iterat...

متن کامل

A Hybrid LQP Alternating Direction Method for Solving Variational Inequality Problems with Separable Structure

In this paper, we presented a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The method generates the new iterate by searching the optimal step size along the descent direction. Global convergence of the new method is proved under certain assumptions.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002