Nonmonotonic projected algorithm with both trust region and line search for constrained optimization

In this paper we combine a reduced Hessian method with a mixed strategy using both trust region and line search techniques for constrained optimization. The adopted strategy switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. By using Fletcherʹs penalty function as a merit function, the resulting algorithm possesses global convergence while maintaining a superlinear local convergence rate under some reasonable conditions. A nonmonotonic criterion is suggested which does not require the merit function to reduce its value after every iteration.