Search

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method 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 filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Abstract: We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd–Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato’s effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. The numerical experiment is reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]