Geodesic
Reduced Hessian methods as a perturbed Newton–Lagrange method
Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 145, pp. 51-64

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For an equality-constrained optimization problem, we consider the possibility to interpret sequential quadratic programming methods employing the Hessian of the Lagrangian reduced to the null space of the constraints’ Jacobian, as a perturbed Newton–Lagrange method. We demonstrate that such interpretation with required estimates on perturbations is possible for certain sequences generated by variants of these methods making use of second-order corrections. This allows to establish, from a general perspective, superlinear convergence of such sequences, the property generally missing for the main sequences of the methods in question.
Keywords: equality-constrained optimization problem, sequential quadratic programming, reduced Hessian of the Lagrangian, perturbed Newton–Lagrange method framework, second-order corrections, superlinear convergence 
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     title = {Reduced {Hessian} methods as a perturbed {Newton{\textendash}Lagrange} method},
     journal = {Vestnik rossijskih universitetov. Matematika},
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     publisher = {mathdoc},
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     number = {145},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2024_29_145_a4/}
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A. A. Volkov; A. F. Izmailov; E. I. Uskov. Reduced Hessian methods as a perturbed Newton–Lagrange method. Vestnik rossijskih universitetov. Matematika, Tome 29 (2024) no. 145, pp. 51-64. http://geodesic.mathdoc.fr/item/VTAMU_2024_29_145_a4/