Geodesic
Multi-step-length gradient iterative method for separable nonlinear least squares problems
Kybernetika, Tome 60 (2024) no. 2, pp. 197-209 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Separable nonlinear least squares (SNLLS) problems are critical in various research and application fields, such as image restoration, machine learning, and system identification. Solving such problems presents a challenge due to their nonlinearity. The traditional gradient iterative algorithm often zigzags towards the optimal solution and is sensitive to the initial guesses of unknown parameters. In this paper, we improve the convergence rate of the traditional gradient method by implementing a multi-step-length gradient iterative algorithm. Moreover, we incorporate the variable projection (VP) strategy, taking advantage of the separable structure observed in SNLLS problems. We propose a multi-step-length gradient iterative-based VP (Mul-GI-VP) method to solve such nonlinear optimization problems. Our simulation results verify the feasibility and high efficiency of the proposed algorithm.
Separable nonlinear least squares (SNLLS) problems are critical in various research and application fields, such as image restoration, machine learning, and system identification. Solving such problems presents a challenge due to their nonlinearity. The traditional gradient iterative algorithm often zigzags towards the optimal solution and is sensitive to the initial guesses of unknown parameters. In this paper, we improve the convergence rate of the traditional gradient method by implementing a multi-step-length gradient iterative algorithm. Moreover, we incorporate the variable projection (VP) strategy, taking advantage of the separable structure observed in SNLLS problems. We propose a multi-step-length gradient iterative-based VP (Mul-GI-VP) method to solve such nonlinear optimization problems. Our simulation results verify the feasibility and high efficiency of the proposed algorithm.
DOI : 10.14736/kyb-2024-2-0197
Classification : 49M99
Keywords: separable nonlinear least squares; multi-step-length gradient iterative method; variable projection algorithm; image restoration 
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     title = {Multi-step-length gradient iterative method for separable nonlinear least squares problems},
     journal = {Kybernetika},
     pages = {197--209},
     year = {2024},
     volume = {60},
     number = {2},
     doi = {10.14736/kyb-2024-2-0197},
     mrnumber = {4757769},
     zbl = {07893454},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-2-0197/}
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Cui, Hai-Rong; Lin, Jing; Su, Jian-Nan. Multi-step-length gradient iterative method for separable nonlinear least squares problems. Kybernetika, Tome 60 (2024) no. 2, pp. 197-209. doi: 10.14736/kyb-2024-2-0197

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