Abstract
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.
Keywords
Sequential quadratic programmingMathematicsLine searchTrust regionIterated functionLimit pointMathematical optimizationNonlinear programmingLimit (mathematics)Filter (signal processing)Convergence (economics)Interior point methodFunction (biology)Quadratic programmingNonlinear systemLine (geometry)Point (geometry)Stationary pointComputer sciencePath (computing)Mathematical analysis
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Publication Info
- Year
- 2005
- Type
- article
- Volume
- 16
- Issue
- 1
- Pages
- 1-31
- Citations
- 388
- Access
- Closed
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Cite This
Andreas Wächter,
Lorenz T. Biegler
(2005).
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence.
SIAM Journal on Optimization
, 16
(1)
, 1-31.
https://doi.org/10.1137/s1052623403426556
Identifiers
- DOI
- 10.1137/s1052623403426556