Crate echidna_optim 

Optimization solvers with automatic differentiation support, plus implicit differentiation tools for differentiating through fixed-point equations.

This crate depends on echidna with the bytecode feature enabled, giving it access to bytecode tapes, forward-over-reverse Hessians, and sparse derivative machinery.

Solvers

Three unconstrained optimizers, all operating on a bytecode-tape Objective:

• L-BFGS (lbfgs) — two-loop recursion limited-memory quasi-Newton. Low per-iteration cost; the default choice for smooth, large-scale problems.
• Newton (newton) — exact Hessian with Cholesky factorization. Quadratic convergence near the solution; practical when n is moderate.
• Trust-region (trust_region) — Steihaug-Toint conjugate-gradient subproblem. Robust on indefinite or ill-conditioned Hessians.

Line search

All solvers use Armijo backtracking (ArmijoParams) to enforce sufficient decrease along the search direction.

Implicit differentiation

Differentiate through solutions of F(z, x) = 0 via the Implicit Function Theorem without unrolling the solver:

• implicit_tangent — tangent (forward) mode: dz/dx · v
• implicit_adjoint — adjoint (reverse) mode: (dz/dx)^T · w
• implicit_jacobian — full Jacobian dz/dx
• implicit_hvp — Hessian-vector product of a loss composed with the implicit solution
• implicit_hessian — full Hessian of a loss composed with the implicit solution

Piggyback differentiation

Differentiate through fixed-point iterations z = G(z, x) by interleaving derivative accumulation with the primal iteration:

• piggyback_tangent_solve — tangent mode (forward)
• piggyback_adjoint_solve — adjoint mode (reverse)
• piggyback_forward_adjoint_solve — interleaved forward-adjoint for second-order derivatives
• piggyback_tangent_step / piggyback_tangent_step_with_buf — single-step building blocks for custom loops

Sparse implicit differentiation

With the sparse-implicit feature, [sparse_implicit] exploits structural sparsity in F_z for efficient implicit differentiation via faer sparse LU factorization. See [SparseImplicitContext], [implicit_tangent_sparse], [implicit_adjoint_sparse], and [implicit_jacobian_sparse].

Re-exports

pub use convergence::ConvergenceParams;

pub use implicit::implicit_adjoint;

pub use implicit::implicit_hessian;

pub use implicit::implicit_hvp;

pub use implicit::implicit_jacobian;

pub use implicit::implicit_tangent;

pub use line_search::ArmijoParams;

pub use objective::Objective;

pub use objective::TapeObjective;

pub use piggyback::piggyback_adjoint_solve;

pub use piggyback::piggyback_forward_adjoint_solve;

pub use piggyback::piggyback_tangent_solve;

pub use piggyback::piggyback_tangent_step;

pub use piggyback::piggyback_tangent_step_with_buf;

pub use result::OptimResult;

pub use result::TerminationReason;

pub use solvers::lbfgs::lbfgs;

pub use solvers::lbfgs::LbfgsConfig;

pub use solvers::newton::newton;

pub use solvers::newton::NewtonConfig;

pub use solvers::trust_region::trust_region;

pub use solvers::trust_region::TrustRegionConfig;

Modules

convergence

implicit

linalg

line_search

objective

piggyback

result

solvers