# Quasi-newton nonlinear solver for sparse jacobian

**URL:** https://discourse.julialang.org/t/quasi-newton-nonlinear-solver-for-sparse-jacobian/57672
**Category:** Optimization (Mathematical)
**Tags:** nonlinear
**Created:** [March 21, 2021, 10:06pm UTC](https://discourse.julialang.org/t/quasi-newton-nonlinear-solver-for-sparse-jacobian/57672 "2021-03-21T22:06:02Z")
**Posts on this page:** 1
**Showing post:** 8

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### Author: ![ctkelley](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ctkelley/32/10684_2.png) [@ctkelley](https://discourse.julialang.org/u/ctkelley)
#### Post date: [March 22, 2021, 12:21am UTC](https://discourse.julialang.org/t/quasi-newton-nonlinear-solver-for-sparse-jacobian/57672/8 "2021-03-22T00:21:18Z")

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BFGS is not a nonlinear solver method. It seeks to maintain a SPD Hessian for optimization. The thing to remember is that **optimization and nonlinear solvers are not the same thing**. Using an algorithm desinged for one of them to solve the other is a bad, bad, bad idea.

Broyden looks for a general low-rank change to an approximate Jacobian and is designed for nonlinear solver applications. Broyden needs a good preconditioner to perform well and has fallen out of favor in the last few decades. Newton-Krylov methods do as well and are more common in modern solvers. The central issue is that quasi-Newton methods, when implemented correctly, consume storage during the nonlinear iteration. Newton-GMRES, for example, consumes storage in the linear iteration and that is far easier to manage and makes nonlinear convergence a simpler problem.

My package (SIAMFANLEquations.jl) has Newton-GMRES working, but the documentation and examples are not really ready for prime time. I’ll have something decent in a month and everything in the master branch works correctly. The latest released version (.0.3.0) works, but the memory allocations are better by far in the master branch.

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