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Add Self-Scaled Broyden (SSBroyden) and SSBFGS optimizers #1658

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@armbrusl

Hi! Id like to propose adding the SSBroyden and SSBFGS optimizers to optax.contrib.

These are full-matrix quasi-Newton methods from Urbán et al. (2025) that use a self-scaled inverse Hessian update. The paper demonstrates strong results on PINNs and similar small-to-medium scale problems.

I've ported the PyTorch implementation from SciMBA to JAX/optax following the existing patterns (scale_by_lbfgs / lbfgs). The implementation includes:

  • ssbroyden() and ssbfgs() as separate public optimizers
  • A shared scale_by_ss_quasi_newton() core transformation
  • Integration with scale_by_zoom_linesearch (same pattern as optax.lbfgs)
  • Tests on quadratic and Rosenbrock functions

I have a working implementation ready. Would you be open to a PR?

Reference:
Urbán, J. F., Stefanou, P., & Pons, J. A. (2025). Unveiling the optimization process of physics informed neural networks: How accurate and competitive can PINNs be? Journal of Computational Physics, 523, 113656. DOI

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