Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming

Andreas Wächter (andreaswwatson.ibm.com)
Lorenz T. Biegler (lb01andrew.cmu.edu)

Abstract: Line search methods for nonlinear programming using Fletcher and Leyffer's filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior point and active set SQP algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. Furthermore, it is shown that the proposed methods do not suffer from the Maratos effect if the search directions are improved by second order corrections, so that fast local convergence to strict local solutions is achieved. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.

Keywords: nonlinear programming, nonconvex constrained optimization, filter method, line search, SQP, interior point, barrier method, global convergence, local convergence, Maratos effect, second order correction

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: CAPD Technical Report B-01-09 (August 2001, revised May 2002) Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA

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Entry Submitted: 08/23/2001
Entry Accepted: 08/23/2001
Entry Last Modified: 05/29/2002

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