This paper presents a modified ODE-based algorithm for unconstrained optimization problems. It combines the idea of IMPBOT algorithm with nonmonotone and subspace techniques. The main feature of this method is that at each iteration, a lower dimensional system of linear equations is solved to obtain a trial step. Under some standard assumptions, the method is proven to be globally convergent. Numerical results show the efficiency of this proposed method in practical computation. [ABSTRACT FROM AUTHOR]
In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter-Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient. [ABSTRACT FROM AUTHOR]