A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties. (English) Zbl 0574.65061

Shultz, Gerald A.; Schnabel, Robert B.; Byrd, Richard H.

SIAM J. Numer. Anal. 22, 47-67 (1985).

The authors present a general class of trust-region-based algorithms for unconstrained minimization. This class also includes line search algorithms. General conditions are given under which limit points of the algorithm will satisfy first and second order necessary conditions for unconstrained minimization. For a wide range of step selection strategies it is shown that the requirements of the convergence theory are satisfied. Several new algorithms are proposed, including an indefinite line search algorithm, several indefinite dogleg algorithms, and a modified ”optimal-step” algorithm.

Reviewer: W.Zulehner

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming

Keywords:

strong global convergence; trust-region-based algorithms; unconstrained minimization; step selection strategies; indefinite dogleg algorithms