Abstract
In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.
| Original language | English |
|---|---|
| Pages (from-to) | 1041-1065 |
| Number of pages | 25 |
| Journal | International Journal of Computer Mathematics |
| Volume | 99 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- 65K05
- 65L09
- 90C30
- Unconstrained optimization
- compressive sensing
- conjugate gradient method
- derivative-free method
- nonlinear equations
- projection method
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics
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