On Lagrange multipliers of trust-region subproblems
Due to their good convergence properties, trust-region methods are widely used. When computing the next iterate, one solves an unconstrained trust-region subproblem that involves also Lagrange multipliers. Several solution approaches, as for example the Steihaug-Toint CG method [\textit{T. Steihaug}, SIAM J. Numer. Anal. 20, 626--637 (1983; Zbl 0518.65042); \textit{Ph. L. Toint}, in: Proc. IMANA Conf., Reading 1980, 57--88 (1981; Zbl 0463.65045)] only require approximations of the Lagrange multipliers. This paper proves a property of the Lagrange multipliers generated when using a Krylov subspace method for the solution of the subproblems. That is, it is shown that the Lagrange multipliers grow monotonically. The paper also suggests improved solution techniques that take this additional property of the Lagrange multipliers into account.
scientific article; zbMATH DE number 5549589