Trust Region Method for Variational Inequality Problem
|School||Nanjing University of Aeronautics and Astronautics|
|Keywords||Trust region methods Non- monotonic adaptive technology Line search technique Box Constrained Variational Inequality D - gap function|
Trust region methods for solving unconstrained optimization problems more effective method , however, has a great impact of the trust region radius selection algorithm is good or bad . The Zhang Xiangsun given an adaptive trust region algorithm , using the current iteration the point of the gradient and Hessian matrix information to select the current iteration step trust region radius , numerical experiments show that this method is more effective than general trust region methods . In this paper, the currently more popular nonmonotonic the proposed nonmonotone adaptive trust region methods improved , thus reducing the amount of computation . Not heavy when tentative step unacceptable solution to the trust region subproblem nonmonotonic line search techniques . General assumptions , not only there is at least an accumulation point for the stable point , but the improved algorithm point column any accumulation point are the stable point of the original problem . In addition, this improved algorithm remains superlinear convergence . This paper not only linearization but linearized constraint set , the set of constraints for a special class of non-empty closed convex subset of variational inequalities into an equivalent set of constraints for multi- surface convex set line variational inequalities sexual variational inequalities , re-use projection and contraction method of calculation . Box Constrained Variational Inequalities converted into equivalent unconstrained optimization problems , recycling Trust Method .