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A Local Convergence Theory of a Filter Line Search Method for Nonlinear Programming

Choong Ming Chin (chin***at***stats.ox.ac.uk)

Abstract: In this paper the theory of local convergence for a class of line search filter type methods for nonlinear programming is presented. The algorithm presented here is globally convergent (see Chin [4]) and the rate of convergence is two-step superlinear. The proposed algorithm solves a sequence of quadratic progrmming subproblems to obtain search directions and instead of using penalty functions to determine the required step size, a filter technique is used to induce convergence. In addition to avoid the Maratos effect, the algorithm also employs second order correction (SOC) steps so that fast local convergence to the solution can be achieved. The proof technique is presented in a fairly general context which allows a range of algorithmic choices associated with choosing the Hessian matrix representation, controlling the step size and feasibility restoration.

Keywords: nonlinear programming, local convergence, line search, filter, multiobjective optimization, SQP

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Numerical Optimization Report, Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, January 2003.

Download: [Postscript]

Entry Submitted: 01/23/2003
Entry Accepted: 01/23/2003
Entry Last Modified: 01/23/2003

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