Module optimize 

Optimization & Root Finding — deterministic numerical solvers.

Determinism Contract

All algorithms in this module are fully deterministic: given the same inputs and the same objective/gradient functions, they produce bit-identical results across runs. Floating-point reductions use binned_sum_f64 from the accumulator module to avoid ordering-dependent rounding.

Scalar Root Finding

• bisect — bisection method (guaranteed convergence for bracketed roots)
• brentq — Brent’s method (IQI + bisection fallback, superlinear convergence)
• newton_scalar — Newton-Raphson (quadratic convergence near root)
• secant — secant method (superlinear convergence, no derivative needed)

Unconstrained Optimization

• minimize_gd — gradient descent with fixed learning rate
• minimize_bfgs — BFGS quasi-Newton with Armijo line search
• minimize_lbfgs — limited-memory BFGS with m history vectors
• minimize_nelder_mead — Nelder-Mead simplex (derivative-free)

Structs

OptResult

Result of an unconstrained optimization run.

Functions

bisect

Bisection method for scalar root finding.

brentq

Brent’s method for scalar root finding.

minimize_bfgs

BFGS quasi-Newton method with Armijo line search.

minimize_gd

Gradient descent with fixed learning rate.

minimize_lbfgs

L-BFGS (limited-memory BFGS) with Armijo line search.

minimize_nelder_mead

Nelder-Mead simplex method (derivative-free).

newton_scalar

Newton-Raphson method for scalar root finding.

penalty_objective

Penalty method for constrained optimization.

project_box

Project a point onto a box constraint [lower, upper].

projected_gd_step

Projected gradient descent step with box constraints.

secant

Secant method for scalar root finding.