Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 150-165
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Local superlinear convergence of the stabilized sequential quadratic programming method is established under very weak assumptions not involving any constraint qualification conditions. However, all attempts to globalize convergence of this method inevitably face principal difficulties related to the behavior of this method when the iterates are still relatively far from solutions. Specifically, the stabilized sequential quadratic programming method has a tendency to generate long sequences of short steps before its superlinear convergence shows up. To that end, the so-called subspace-stabilized sequential quadratic programming method has been proposed, demonstrating better “semi-local” behavior, and hence, more suitable for development of practical algorithms on its basis. In this work we propose two techniques for hybrid globalization of convergence of this method: algorithm with backups, and algorithm with records.We provide theoretical results on convergence and rate of convergence of these algorithms, as well as some results of their numerical testing.
Keywords:
sequential quadratic programming, degenerate solutions, noncritical Lagrange multiplier, dual stabilization, globalization of convergence.
@article{VTAMU_2019_24_126_a1,
author = {N. G. Zhurbenko and A. F. Izmailov and E. I. Uskov},
title = {Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method},
journal = {Vestnik rossijskih universitetov. Matematika},
pages = {150--165},
publisher = {mathdoc},
volume = {24},
number = {126},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a1/}
}
TY - JOUR AU - N. G. Zhurbenko AU - A. F. Izmailov AU - E. I. Uskov TI - Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method JO - Vestnik rossijskih universitetov. Matematika PY - 2019 SP - 150 EP - 165 VL - 24 IS - 126 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a1/ LA - ru ID - VTAMU_2019_24_126_a1 ER -
%0 Journal Article %A N. G. Zhurbenko %A A. F. Izmailov %A E. I. Uskov %T Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method %J Vestnik rossijskih universitetov. Matematika %D 2019 %P 150-165 %V 24 %N 126 %I mathdoc %U http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a1/ %G ru %F VTAMU_2019_24_126_a1
N. G. Zhurbenko; A. F. Izmailov; E. I. Uskov. Hybrid globalization of convergence of subspace-stabilized sequential quadratic programming method. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 150-165. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a1/