Geodesic
Hybrid globalization of convergence of the Levenberg-Marquardt method for equality-constrained optimization problems
Vestnik rossijskih universitetov. Matematika, Tome 30 (2025) no. 149, pp. 41-55

Voir la notice de l'article provenant de la source Math-Net.Ru

The Levenberg–Marquardt method possesses local superlinear convergence for general systems of nonlinear equations under weal assumptions allowing for nonisolated solutions. This justifies its application to first-order optimality systems of constrained optimization problems with possibly violated constraint qualifications, the latter giving rise to nonuniqueness of Lagrange multipliers. However, the existing strategies for globalization of convergence of the Levenberg–Marquardt method are not optimization-oriented by nature, i. e., when applied to optimization problems, they are intended not for finding solutions, but rather any stationary points of such problems. In this work, we propose optimization-oriented globalization strategies for the Levenberg–Marquardt method applied to optimization problems with equality constraints. The proposed strategies are hybrid by their character, i. e., they combine a globally convergent optimization outer phase method with asymptotic switching to the Levenberg–Marquardt method. Global convergence properties and superlinear rate of convergence are established. Numerical results are provided, demonstrating that the proposed hybrid algorithms are workable.
Keywords: equality-constrained optimization problem, Lagrange optimality system, globalization with backups, globalization with records
Mots-clés : Levenberg–Marquardt method 
@article{VTAMU_2025_30_149_a3,
     author = {A. F. Izmailov and E. I. Uskov},
     title = {Hybrid globalization of convergence of the {Levenberg-Marquardt} method for equality-constrained optimization problems},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {41--55},
     publisher = {mathdoc},
     volume = {30},
     number = {149},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2025_30_149_a3/}
}
TY  - JOUR
AU  - A. F. Izmailov
AU  - E. I. Uskov
TI  - Hybrid globalization of convergence of the Levenberg-Marquardt method for equality-constrained optimization problems
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2025
SP  - 41
EP  - 55
VL  - 30
IS  - 149
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2025_30_149_a3/
LA  - ru
ID  - VTAMU_2025_30_149_a3
ER  - 
%0 Journal Article
%A A. F. Izmailov
%A E. I. Uskov
%T Hybrid globalization of convergence of the Levenberg-Marquardt method for equality-constrained optimization problems
%J Vestnik rossijskih universitetov. Matematika
%D 2025
%P 41-55
%V 30
%N 149
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTAMU_2025_30_149_a3/
%G ru
%F VTAMU_2025_30_149_a3
A. F. Izmailov; E. I. Uskov. Hybrid globalization of convergence of the Levenberg-Marquardt method for equality-constrained optimization problems. Vestnik rossijskih universitetov. Matematika, Tome 30 (2025) no. 149, pp. 41-55. http://geodesic.mathdoc.fr/item/VTAMU_2025_30_149_a3/