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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]

In this article, we consider the problem of finding a solution of a nonsmooth constrained (and not necessarily square) system of equations. We first reformulate the original problem as an equivalent system of equations with nonnegative constraints, and then present a smoothing projected Levenberg-Marquardt type algorithm to solve the reformulated system, which solves a strictly convex quadratic program at each iteration. We show that this algorithm not only converges globally, but also converges locally superlinearly under an error bound assumption that is much weaker than the standard nonsingularity condition. Some numerical results for the presented algorithm indicate that the algorithm works quite well in practice. [ABSTRACT FROM PUBLISHER]

The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization. The feasibility restoration phase, which is always used in the traditional filter method, is not needed. Under mild conditions, global convergence and local superlinear convergence rates are obtained. Numerical results demonstrate that the new algorithm is effective. [ABSTRACT FROM AUTHOR]