Convergence of a Solution Algorithm in Indefinite Quadratic Programming
Abstract
It is proved that, for an indefinite quadratic programming problem under linear constraints, any iterative sequence generated by the Proximal DC decomposition algorithm -linearly converges to a Karush-Kuhn-Tucker point, provided that the problem has a solution. Another major result of this paper says that DCA sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably-chosen neighborhood of it. To deal with the implicitly defined iterative sequences, a local error bound for affine variational inequalities and novel techniques are used. Numerical results together with an analysis of the influence of the decomposition parameter, as well as a comparison between the Proximal DC decomposition algorithm and the Projection DC decomposition algorithm, are given in this paper. Our results complement a recent and important paper of Le Thi, Huynh, and Pham Dinh (J. Optim. Theory Appl. 179 (2018), 103-126).
Cite
@article{arxiv.1810.02044,
title = {Convergence of a Solution Algorithm in Indefinite Quadratic Programming},
author = {Tran Hung Cuong and Yongdo Lim and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:1810.02044},
year = {2018}
}