A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications

Maaz ur Rehman, Jamilu Sabi’u, Muhammad Sohaib, Abdullah Shah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The nonlinear programming makes use of quasi-Newton methods, a collection of optimization approaches when traditional Newton’s method are challenging due to the calculation of the Jacobian matrix and its inverse. Since the Jacobian matrix is computationally difficult to compute and sometimes not available specifically when dealing with non-smooth monotone systems, quasi-Newton methods with superlinear convergence are preferred for solving nonlinear system of equations. This paper provides a new version of the derivative-free David–Fletcher–Powell (DFP) approach for dealing with nonlinear monotone system of equations with convex constraints. The optimal value of the scaling parameter is found by minimizing the condition number of the DFP matrix. Under certain assumptions, the proposed method has global convergence, required minimal storage and is derivative-free. When compared to standard methods, the proposed method requires less iteration, function evaluations, and CPU time. The image restoration test problems demonstrate the method’s reliability and efficiency.

Original languageEnglish
Pages (from-to)3645-3673
Number of pages29
JournalJournal of Applied Mathematics and Computing
Volume69
Issue number5
DOIs
StatePublished - Oct 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.

Keywords

  • Condition number
  • Global convergence
  • Image restoration
  • Nonlinear convex constraint monotone equations
  • Projection-based approach
  • Quasi-Newton methods
  • Scaled DFP formula

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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