On Lagrange multipliers of trust-region subproblems

Ctirad Matonoha, Ladislav Luksan a Jan Vlcek

Trust-region methods are globally convergent techniques widely used,
for example, in connection with the Newton's method for unconstrained
optimization. One of the most commonly-used iterative approaches for
solving the trust-region subproblems is the Steihaug-Toint method
which is based on conjugate gradient iterations and seeks a solution
on Krylov subspaces. We will give a theory concerning properties of
Lagrange multipliers obtained on these subspaces.