A dwindling filter inexact projected Hessian algorithm for large scale nonlinear constrained optimization

In this paper, we propose a dwindling filter inexact projected Hessian algorithm for solving large scale nonlinear constrained optimization. For large-scale applications, inexact projected Hessian algorithm is needed to get search direction by solving one or more linear systems approximately using iterative linear algebra techniques. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero so that the new filter has more flexibility for the acceptance of the trial step compared with traditional filter. Under mild conditions, global convergence and local superlinear convergence rate are obtained. The numerical experiments are reported to show the effectiveness of the proposed algorithm for large scale problems.