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This paper presents a trust-region algorithm which employs line search filter technique with Lagrange merit function for solving nonlinear equality constrained programming. At the current iteration, the general full trust-region subproblem is decomposed into a pair of trust-region subproblems in normal and tangential subspaces. The trial step is given by solving these two trust-region subproblems. Then, different from traditional trust-region method in which the next iterate is determined by the ratio of the actual reduction to the predicted reduction, the step size is decided by interior backtracking line search together with filter method. Consequently, the expensive computation raised by resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be reduced. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. The new method retains the global convergence to the first-order critical points under some reasonable assumptions without using a merit function. Meanwhile, by using Lagrange function in the filter, the method can overcome Maratos effect without using second order correction step and hence the superlinear local convergence is achieved. The preliminary numerical results are reported to show effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop dwindling filter idea and trust region strategy for solving nonlinear optimization. Compared with traditional filter trust region algorithm, the new filter algorithm has more flexibility for the acceptance of the trial step and the feasibility restoration phase is not needed. Under mild conditions, the global convergence of the new algorithm is analyzed. Preliminary numerical results are reported. [Copyright &y& Elsevier]

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]

Abstract: Filter methods were initially designed for nonlinear programming problems by Fletcher and Leyffer. In this paper we propose a secant algorithm with line search filter method for nonlinear equality constrained optimization. The algorithm yields the global convergence under some reasonable conditions. By using the Lagrangian function value in the filter we establish that the proposed algorithm can overcome the Maratos effect without using second order correction step, so that fast local superlinear convergence to second order sufficient local solution is achieved. The primary numerical results are presented to confirm the robustness and efficiency of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonmonotone sequential quadratic programming-filter method for solving nonlinear equality constrained optimization. This new method has more flexibility for the acceptance of the trial step and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the global convergence properties. Further, the second-order correction step and nonmonotone reduction conditions are used to overcome Maratos effect so that quadratic local convergence is achieved. The numerical experiments are reported to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

In this paper we propose a two-piece update of projected Hessian algorithm with trust region method for solving nonlinear equality constrained optimization problems. In order to deal with large scale problems, a two-piece update of two side reduced Hessian is used to replace full Hessian matrix. By adopting the l1 penalty function as the merit function, a nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. The calculation of a correction step, which is necessary from theoretical point to overcome Maratos effect but sometime brings in negative results in practice, is avoided in most cases by setting a criterion to judge its necessity. The proposed algorithm which switches to nonmonotonic trust region strategy possess global convergence while maintaining one-step Q-superlinear local convergence rates if at least one of the update formula is updated at each iteration. The numerical experiment is reported to show the effectiveness of the proposed algorithms. [Copyright &y& Elsevier]