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

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].


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