Error bounds and superlinear convergence analysis of some Newton-type methods in optimization. (English) Zbl 0965.65091

Tseng, Paul

Di Pillo, Gianni (ed.) et al., Nonlinear optimization and related topics. Workshop, Erice, Sicily, Italy, June 23-July 2, 1998. Dordrecht: Kluwer Academic Publishers. Appl. Optim. 36, 445-462 (2000).

Summary: We show that, for some Newton-type methods such as primal-dual interior-point following methods and of C. Chen and O. L. Mangasarian [Math. Program. 71A, No. 1, 51-69 (1995; Zbl 0855.90124); Comput. Optim. Appl. 5, No. 2,57-138 (1996; Zbl 0859.90112)], smoothing methods the local superlinear convergence can be shown without assuming the solutions are isolated. The analysis is based on local error bounds on the distance from the iterates to the solution set.
For the entire collection see [Zbl 0949.00039].

MSC:

65K05	Numerical mathematical programming methods
90C34	Semi-infinite programming
90C51	Interior-point methods

Keywords:

error bound; superlinear convergence; Newton method; continuation/smoothing method; interior-point method; complementarity problem

Citations:

Zbl 0855.90124; Zbl 0859.90112