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Abstract
Conn, Gould, and Toint have proposed a class of trust region algorithms for minimizing nonlinear functions whose variables are subjected to simple bound constraints. In their convergence analysis, they show that if the strict complementarity condition holds, the considered algorithms reduce to an unconstrained calculation after finitely many iterations, allowing fast asymptotic rates of convergence. This paper analyses the behaviour of these iterative processes in the case where the strict complementarity condition is violated. It is proved that inexact Newton methods lead to superlinear or quadratic rates of convergence, even if the set of active bounds at the solution is not entirely detected. Practical criteria for stopping the inner iterations of the algorithms are deduced, ensuring these rates of convergence.
Original language | English |
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Pages (from-to) | 476-495 |
Number of pages | 20 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 28 |
Issue number | 2 |
Publication status | Published - 1 Apr 1991 |
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LANCELOT: LANCELOT, a package for the solution of large-scale nonlinear optimization problems
TOINT, P., Sartenaer, A., Gould, N. I. M. & Conn, A.
1/09/87 → 1/09/00
Project: Research
Student theses
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Trust-region methods and degenerate problems
Author: Lescrenier, M., 1989Supervisor: Toint, P. (Supervisor)
Student thesis: Doc types › Doctor of Sciences