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Self-Scaled Broyden Family of Quasi-Newton Methods in JAX

Ivan Bioli, Mikel Mendibe Abarrategi

Abstract

We present a JAX implementation of the Self-Scaled Broyden family of quasi-Newton methods, fully compatible with JAX and building on the Optimistix~\cite{rader_optimistix_2024} optimisation library. The implementation includes BFGS, DFP, Broyden and their Self-Scaled variants(SSBFGS, SSDFP, SSBroyden), together with a Zoom line search satisfying the strong Wolfe conditions. This is a short technical note, not a research paper, as it does not claim any novel contribution; its purpose is to document the implementation and ease the adoption of these optimisers within the JAX community. The code is available at https://github.com/IvanBioli/ssbroyden_optimistix.git.

Self-Scaled Broyden Family of Quasi-Newton Methods in JAX

Abstract

We present a JAX implementation of the Self-Scaled Broyden family of quasi-Newton methods, fully compatible with JAX and building on the Optimistix~\cite{rader_optimistix_2024} optimisation library. The implementation includes BFGS, DFP, Broyden and their Self-Scaled variants(SSBFGS, SSDFP, SSBroyden), together with a Zoom line search satisfying the strong Wolfe conditions. This is a short technical note, not a research paper, as it does not claim any novel contribution; its purpose is to document the implementation and ease the adoption of these optimisers within the JAX community. The code is available at https://github.com/IvanBioli/ssbroyden_optimistix.git.
Paper Structure (5 sections, 7 equations, 1 figure, 1 table)

This paper contains 5 sections, 7 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The Self-Scaled Broyden Family
  3. Software Design
  4. Numerical Example: PINNs for the 3D Poisson Equation
  5. Acknowledgements

Figures (1)

  • Figure 1: Convergence of quasi-Newton solvers on the 3D Poisson PINN problem. The self-scaled variants (SSBFGS, SSBroyden) achieve lower errors in fewer iterations compared to the standard BFGS and Broyden methods.