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Result: Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence: Line search filter methods for nonlinear programming: motivation and global convergence

Title:
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence: Line search filter methods for nonlinear programming: motivation and global convergence
Authors:
Lorenz T. Biegler, Andreas Wächter
Source:
SIAM Journal on Optimization. 16:1-31
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2005.
Publication Year:
2005
Subject Terms:
Numerical methods based on nonlinear programming, filter method, 0211 other engineering and technologies, Interior-point methods, 02 engineering and technology, nonconvex constrained optimization, 01 natural sciences, Methods of successive quadratic programming type, global convergence, Numerical mathematical programming methods, Nonlinear programming, interior point method, nonlinear programming, barrier method, line search, 0101 mathematics, sequential quadratic programming
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1095-7189
1052-6234
DOI:
10.1137/s1052623403426556
Access URL:
https://zbmath.org/2206226
https://doi.org/10.1137/s1052623403426556
Accession Number:
edsair.doi.dedup.....ac4ae4010f8fdbf53b4c420e3d82b4f9
Database:
OpenAIRE

Further Information

Summary: Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [\textit{R. Flechter} and \textit{S. Leyffer}, Math. Program. 91, No. 2 (A), 239--269 (2002; Zbl 1049.90088)], 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.