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Optimization algorithms are designed to find optimal solutions by minimizing or maximizing an objective function subject to constraints. The objective function, which may be non-linear, complex, or non-differentiable, defines the relationship between the system parameters and the desired outcome. This work focuses on numerical optimization techniques, specifically comparing the efficiency of Gradient Descent (GD), Broyden-Fletcher-Goldfarb-Shanno (BFGS), and Limited-memory BFGS (LBFGS) algorithms for problems arising from inverse or ill-conditioned scenarios.

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A Deep Numerical Study of BFGS and LBFGS Methods for Solving Optimization Problems Arising from Inverse Applications

  • 会议论文

  • 发表日期：

    2025年

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  • Mohamed Ziouane,
  • Hafida Hamdi,
  • Mourad Nachaoui,
  • Abdeljalil Nachaoui

摘要

Optimization algorithms are designed to find optimal solutions by minimizing or maximizing an objective function subject to constraints. The objective function, which may be non-linear, complex, or non-differentiable, defines the relationship between the system parameters and the desired outcome. This work focuses on numerical optimization techniques, specifically comparing the efficiency of Gradient Descent (GD), Broyden-Fletcher-Goldfarb-Shanno (BFGS), and Limited-memory BFGS (LBFGS) algorithms for problems arising from inverse or ill-conditioned scenarios.