opt

tangent/opt validated against scipy.optimize

Numerical optimization: function minimization, curve fitting, and root finding. Derivative-free and gradient-based methods share one declarative interface, and gradients are optional (supply them, return them from the objective, or let finite differences fill in).

npm install @tangent.to/opt      # npm
deno add jsr:@tangent/opt        # Deno / JSR

Run the example notebook

Minimization

The declarative entry point takes a single spec object and dispatches by method. L-BFGS is the default for smooth problems; Nelder-Mead needs no gradient. An objective may return a number, { loss, gradient }, or { value, gradient } as grad’s valueAndGrad and compile do, so one of those is an objective as it stands.

Signature	Description
`minimize({ f, x0, method, grad?, bounds? })`	Minimize a scalar function of several variables. Returns `{ x, fx, converged, nfev, iterations }`.
`lbfgs(f, x0, options?)`	Limited-memory quasi-Newton with a strong-Wolfe line search.
`nelderMead(f, x0, options?)`	Derivative-free downhill simplex.
`gradientDescent(f, x0, options?)`	Gradient descent with optional backtracking line search.
`adam(f, x0, options?)`	Adam, for stochastic or noisy objectives.
`adamStep(x, gradient, state, options)`	One Adam update in place, for a loop that owns its own sampling; `state` is created on the first call. Also `gradientStep`, `momentumStep`, `rmspropStep`. The drivers above are built from these.
`methods()`	List the available method names.

Scalar problems

Signature	Description
`minimizeScalar(f, options?)`	Brent minimization on a one-dimensional function, with automatic bracketing.
`rootScalar(f, options?)`	Brent-Dekker root finding on a bracketed sign change.

Curve fitting and least squares

Signature	Description
`curveFit({ f, xdata, ydata, p0, bounds?, loss? })`	Fit a model to data. Returns parameters, covariance and standard errors. Robust losses (`huber`, `soft_l1`, `cauchy`) resist outliers.
`leastSquares({ residual, x0, jac?, bounds? })`	Nonlinear least squares (Levenberg-Marquardt).

Gradients and bounds

Signature	Description
`numericalGradient(f, x, h?)`	Central finite-difference gradient.
`numericalJacobian(f, x, h?)`	Central finite-difference Jacobian.
`numericalHessian(f, x, h?)`	Central finite-difference Hessian.
`makeBoundsTransform(bounds)`	Box-bounds transform shared by every method.

Verified against scipy

The comparison suite runs every method against scipy.optimize on shared problems: L-BFGS matches L-BFGS-B to within its own tolerance, curveFit recovers parameters and standard errors that agree with curve_fit, and rootScalar matches brentq to machine precision. Under three gross outliers a plain fit’s slope collapses while the Huber-robust fit holds it near the true value.