A Derivative-Free Multivariate Spectral Projection Algorithm for Constrained NonLinear Monotone Equations

Hassan Mohammad*, Mohammed Yusuf Waziri, Auwal Bala Abubakar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper, we present a derivative-free multivariate spectral projection algorithm for convex constrained nonlinear monotone equations. The search direction is a product of a convex combination of two different spectral diagonal matrices and the residual vector. Moreover, to ensure positive definiteness of the diagonal matrix associated with the search direction, suitable safeguard is formulated. Some of the remarkable properties of the algorithm include: Jacobian free approach, capacity to solve large-scale problems and the search direction generated by the algorithm, satisfy the descent property independent on the line search employed. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show that the algorithm has advantages over the recently proposed multivariate derivative-free projection algorithm by Liu and Li (J Ind Manag Optim 13(1):283–295, 2017) and also compete with another algorithm having the standard choice of the Barzilai-Borwein step as the search direction.

Original languageEnglish
Article number55
JournalInternational Journal of Applied and Computational Mathematics
Issue number2
Publication statusPublished - Apr 2021
Externally publishedYes


  • Derivative-free method
  • Global convergence
  • Multivariate spectral method
  • Nonlinear monotone equations
  • Projection method


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