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Zbl 1114.90128
Wächter, Andreas; Biegler, Lorenz T.
Line search filter methods for nonlinear programming: motivation and global convergence. (English)
[J] SIAM J. Optim. 16, No. 1, 1-31 (2005). ISSN 1052-6234; ISSN 1095-7189/e

Summary: Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [{\it R. Flechter} and {\it 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.

MSC 2000:: *90C30 Nonlinear programming
49M37 Methods of nonlinear programming type
65K05 Mathematical programming (numerical methods)
90C51 Interior-point methods
90C55 Methods of successive quadratic programming type

Keywords: nonlinear programming; nonconvex constrained optimization; filter method; line search; sequential quadratic programming; interior point method; barrier method; global convergence

Citations: Zbl 1049.90088

Cited in: Zbl 1208.49040 Zbl 1207.49039 Zbl 1115.90056

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