Fides.jl

Fides.jl is a Julia wrapper of the Python package Fides.py, which implements an Interior Trust Region Reflective algorithm for bounds constrained optimization problems based on [1, 2]. Fides targets problems on the form:

$$\min_{x \in \mathbb{R}^n} f(x) \quad \mathrm{subject \ to} \quad \text{lb} \leq x \leq \text{ub}$$

Where f is a continues at least twice-differentiable function, and lb and ub are the lower and upper bounds respectively.

Main features

• Boundary-constrained interior trust-region optimization.
• Recursive reflective and truncated constraint management.
• Full and 2D subproblem solution solvers.
• Supports used provided Hessian, as well as BFGS, DFP, and SR1 Hessian approximations.
• Good performance for parameter estimating Ordinary Differential Equation models [3].

Additional information and tutorials can be found in the documentation.

Citation

If you found Fides useful in your work, please cite the following paper:

@article{2022fides,
  title={Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models},
  author={Fr{\"o}hlich, Fabian and Sorger, Peter K},
  journal={PLoS computational biology},
  volume={18},
  number={7},
  pages={e1010322},
  year={2022},
  publisher={Public Library of Science San Francisco, CA USA}
}

References

1. Coleman, T. F., & Li, Y. (1994). On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Mathematical programming, 67(1), 189-224.
2. Coleman, T. F., & Li, Y. (1996). An interior trust region approach for nonlinear minimization subject to bounds. SIAM Journal on optimization, 6(2), 418-445.
3. Fröhlich, F., & Sorger, P. K. (2022). Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models. PLoS computational biology, 18(7), e1010322.