New parameter-free fixed-point algorithms achieve linear convergence

Researchers have developed new parameter-free fixed-point algorithms designed for contractive mappings. These algorithms can automatically identify and leverage hidden contractivity without needing prior knowledge of the contraction factor. The methods offer explicit linear convergence rates for both the fixed-point residual and the distance to the unique fixed point, while maintaining computational costs similar to classical fixed-point schemes. Extensions include applications to co-coercive equations and parameter-free accelerated variants inspired by Nesterov's schemes, with numerical experiments showing competitive performance against existing adaptive methods. AI

IMPACT Introduces novel algorithmic techniques that could enhance optimization processes in machine learning and other AI applications.

RANK_REASON Academic paper detailing new algorithms and theoretical convergence rates. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• Halpern fixed-point iteration
• Nesterov's accelerated fixed-point schemes
• Tikhonov regularization

• paper
• other

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →