Local convergence of a line search filter sequential adaptive cubic regularization algorithm for nonlinear constrained optimization

An adaptive regularisation algorithm using cubics (ARC) in association with the line search filter technique for solving nonlinear equality constrained programming is proposed in this paper.In each iteration, the trial step providing sufficient descent is generated by solving a corresponding ARC subproblem.Then, the step size is decided by backtracking line search together with the filter technique to obtain the next iteration point.The advantage of this method is that resolving ARC subproblem many times to determine a new iteration point can be avoided and hence the expensive computation can be lessened.And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using the filter technique.Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect.Convergence analysis demonstrates that fast local convergence can be achieved under some mild assumptions.The preliminary numerical results are reported.