A filter secant method with nonmonotone line search for equality constrained optimization

This paper proposes a filter secant method with nonmonotone line search for non- linear equality constrained optimization. The Hessian of the Lagrangian is approximated using the BFGS secant update. This new method has more flexibility for the acceptance of the trial step and requires less computational costs compared with themonotone one. The global and local convergence of the proposed method are given under some reasonable conditions. Further, two-step Q-superlinear convergence rate is established by introducing second order correction step. The numerical experiments are reported to show the effectiveness of the proposed algorithm.