Line search filter methods for nonlinear programming: motivation and global convergence. (English) Zbl 1114.90128

Wächter, Andreas; Biegler, Lorenz T.

SIAM J. Optim. 16, No. 1, 1-31 (2005).

Summary: Line search methods are proposed for nonlinear programming using Fletcher and Leyffer’s filter method [R. Flechter and 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:

90C30	Nonlinear programming
49M37	Numerical methods based on nonlinear programming
65K05	Numerical mathematical programming 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

Software:

Ipopt; ipfilter