Gradient projection method on the sphere, complementarity problems and copositivity

Orizon Ferreira, Yingchao Gao, Sandor Nemeth*, Petra Renáta Rigó

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalJournal of Global Optimization
Volume90
Issue number1
Early online date16 Apr 2024
DOIs
Publication statusPublished - 1 Sept 2024

Keywords

  • Gradient projection method on the sphere
  • Copositivity
  • Nonlinear cone-complementarity problems
  • 90C30
  • 90C33

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