On Lagrange multipliers of trust-region subproblems

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 trust-region subproblems is the Steihaug–Toint method which is based on conjugate gr...

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Veröffentlicht in:	BIT (Nordisk Tidskrift for Informationsbehandling) 2008-12, Vol.48 (4), p.763-768
Hauptverfasser:	Lukšan, L., Matonoha, C., Vlček, J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus of variations and optimal control Computational Mathematics and Numerical Analysis Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Mathematics and Statistics Numeric Computing Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Beschreibung
Zusammenfassung:	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 trust-region subproblems is the Steihaug–Toint method which is based on conjugate gradient iterations and seeks a solution on Krylov subspaces. This paper contains new theoretical results concerning properties of Lagrange multipliers obtained on these subspaces.
ISSN:	0006-3835 1572-9125
DOI:	10.1007/s10543-008-0197-5