Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence

Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [Math. Program., 91 (2002), pp. 239--269], which replaces the traditional merit function. Their global convergence properties are analyzed. The presented framework is applied to active set sequ...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 16; no. 1; pp. 1 - 31
Main Authors: Wächter, Andreas, Biegler, Lorenz T.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2005
Subjects:
Algorithms
Methods
Motivation
Optimization
Quadratic programming
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [Math. Program., 91 (2002), pp. 239--269], which replaces the traditional merit function. Their global convergence properties are analyzed. The presented framework is applied to active set sequential quadratic programming (SQP) and barrier interior point 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. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.
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ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623403426556