domains / families / science / nonlinear-solvers

nonlinear-solvers

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Select and configure nonlinear solvers for f(x)=0 or min F(x). Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.

When to use

• Newton methods
• quasi-Newton (BFGS, L-BFGS)
• Broyden
• Anderson acceleration
• diagnosing convergence issues
• choosing line search vs trust region
• analyzing Jacobian quality

When not to use

• **No global convergence guarantee**: All methods may fail for pathological problems
• **Jacobian accuracy**: Finite-difference Jacobian may be inaccurate near discontinuities
• **Large dense problems**: May require specialized solvers not covered here
• **Constrained optimization**: Complex constraints need SQP or interior point methods

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