A framework for proving global convergence for a class of line search filter type methods for nonlinear programming is presented. The underlying method is based on the dominance concept of multiobjective optimization where trial points are accepted provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve a sequence of quadratic programming subproblems for which effective software is readily available, and instead of using trust region strategies, the methods utilize line search techniques to induce global convergence. The proof technique is presented in a fairly general context, allowing a range of specific algorithm choices associated with choosing the Hessian matrix representation, controlling the step size and feasibility restoration.
Numerical Optimization Report, September 2002
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