Gradient projection method on the sphere, complementarity problems and copositivity

Ferreira, Orizon Pereira, Gao, Yingchao, Németh, Sándor Zoltán and Rigó, Petra Renáta (2024) Gradient projection method on the sphere, complementarity problems and copositivity. Journal of Global Optimization . DOI https://doi.org/10.1007/s10898-024-01390-4

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Official URL: https://doi.org/10.1007/s10898-024-01390-4

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.

Item Type:

Article

Divisions:

Institute of Operations and Decision Sciences

Subjects:

Mathematics, Econometrics

Projects:

CNPq grants 305158/2014-7, CNPq grants 302473/2017-3, FAPEG/PRONEM- 201710267000532, ÚNKP-22-4 New National Excellence Program, NKFIH 142154

DOI:

https://doi.org/10.1007/s10898-024-01390-4

ID Code:

9838