We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1081,
author = {Agnieszka Prusi\'nska and Alexey Tret'yakov},
title = {On existence of solutions to degenerate nonlinear optimization problems},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {27},
year = {2007},
pages = {151-164},
zbl = {1151.90048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1081}
}
Agnieszka Prusińska; Alexey Tret'yakov. On existence of solutions to degenerate nonlinear optimization problems. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 27 (2007) pp. 151-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1081/
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