Solving KKT Systems via the Trust Region and the ConjugateGradient Methods 1

In this paper, we propose a trust region method for solving KKT systems arising from the variational inequality problem and the constrained optimization problem. The trust region subproblem is derived from reformulation of the KKT system as a constrained optimization problem and is solved by the truncated conjugate gradient method; meanwhile the variables remain feasible with respect to the constrained optimization problem. Global and superlinear convergence are established. Some preliminary numerical experiments show that the method is quite promising.

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