@article{ce2225f9185340c8963632cdcb6a8ac3,
title = "Gradient projection method on the sphere, complementarity problems and copositivity",
abstract = "By using a constant step-size, the convergence analysis of the gradient projection method on the sphere is presented for a closed spherically convex set. This algorithm is applied to discuss copositivity of operators with respect to cones. This approach can also be used to analyse solvability of nonlinear cone-complementarity problems. To our best knowledge this is the first numerical method related to the copositivity of operators with respect to the positive semidefinite cone. Numerical results concerning the copositivity of operators are also provided.",
author = "Orizon Ferreira and Yingchao Gao and Sandor Nemeth and Rig{\'o}, {Petra Ren{\'a}ta}",
note = "O. P. Ferreira was supported in part by CNPq grants 305158/2014-7 and 302473/2017-3, FAPEG/PRONEM- 201710267000532 and CAPES. The research of P.R. Rig{\'o} has been supported by the {\'U}NKP-22-4 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund. Petra Ren{\'a}ta Rig{\'o} is thankful for the support provided by the Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund, financed under the PD_22 funding scheme, project no. 142154. The authors also want to thank the referees for the valuable suggestions and prof. Gabrielle Eichfelder, prof. Janez Povh and prof. Zsolt Darvay for sharing the matrices for copositive tests in Sect. 5.1.2.",
year = "2024",
month = apr,
day = "16",
doi = "10.1007/s10898-024-01390-4",
language = "English",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer",
}