106. A Hybrid Conjugate Gradient-Like Algorithm for Solving Nonlinear Equations and Image Restoration
Invited abstract in session WC-7: Numerical Methods and Applications II, stream Numerical Methods and Applications.
Wednesday, 14:00-16:00Room: B100/5015
Authors (first author is the speaker)
| 1. | Supak Phiangsungnoen
|
| Mathematics, Rajamangala University of Technology Rattanakosin |
Abstract
In this work, we present a hybrid spectral-conjugate gradient (SCG) method designed to efficiently solve nonlinear monotone operator equations. Our approach integrates a hybrid parameter that unifies key conjugate gradient methods, including Polak–Ribière–Polyak (PRP), Liu-Storey (LS), Fletcher-Reeves (FR), and conjugate descent (CD), as special cases. To ensure that the search direction satisfies the sufficient descent condition, we derive an appropriate spectral parameter. Additionally, the search direction is constructed to remain bounded, and under specific conditions, we establish the convergence of the sequence generated by our hybrid SCG algorithm. To demonstrate its effectiveness, we conduct extensive numerical experiments comparing the proposed method with existing algorithms. These experiments, based on benchmark nonlinear monotone operator equations, highlight the superior efficiency and practical potential of our approach.
Keywords
- Applications of continuous optimization
- Linear and nonlinear optimization
- Computational mathematical optimization
Status: accepted
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