A linearly convergent derivative-free descent method for strongly monotonecomplementarity problems

Citation
Ol. Mangasarian et Mv. Solodov, A linearly convergent derivative-free descent method for strongly monotonecomplementarity problems, COMPUT OP A, 14(1), 1999, pp. 5-16
Citations number
43
Categorie Soggetti
Engineering Mathematics
Journal title
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
ISSN journal
09266003 → ACNP
Volume
14
Issue
1
Year of publication
1999
Pages
5 - 16
Database
ISI
SICI code
0926-6003(199907)14:1<5:ALCDDM>2.0.ZU;2-T
Abstract
We establish the first rate of convergence result for the class of derivati ve-free descent methods for solving complementarity problems. The algorithm considered here is based on the implicit Lagrangian reformulation [26, 35] of the nonlinear complementarity problem, and makes use of the descent dir ection proposed in [42], but employs a different Armijo-type linesearch rul e. We show that in the strongly monotone case, the iterates generated by th e method converge globally at a linear rate to the solution of the problem.