## Abstract

In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.

Original language | English |
---|---|

Article number | 1221 |

Journal | Mathematics |

Volume | 11 |

Issue number | 5 |

DOIs | |

State | Published - Mar 2023 |

### Bibliographical note

Publisher Copyright:© 2023 by the authors.

## Keywords

- convex constraints
- image restoration
- measure function
- memoryless DFP algorithm
- one-parameter scaling

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)