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Optimization and root finding (scipy.optimize)

Optimization

General-purpose

minimize(fun, x0[, args, method, jac, hess, ...])	Minimization of scalar function of one or more variables.
fmin(func, x0[, args, xtol, ftol, maxiter, ...])	Minimize a function using the downhill simplex algorithm.
fmin_powell(func, x0[, args, xtol, ftol, ...])	Minimize a function using modified Powell’s method. This method
fmin_cg(f, x0[, fprime, args, gtol, norm, ...])	Minimize a function using a nonlinear conjugate gradient algorithm.
fmin_bfgs(f, x0[, fprime, args, gtol, norm, ...])	Minimize a function using the BFGS algorithm.
fmin_ncg(f, x0, fprime[, fhess_p, fhess, ...])	Unconstrained minimization of a function using the Newton-CG method.
leastsq(func, x0[, args, Dfun, full_output, ...])	Minimize the sum of squares of a set of equations.

Constrained (multivariate)

fmin_l_bfgs_b(func, x0[, fprime, args, ...])	Minimize a function func using the L-BFGS-B algorithm.
fmin_tnc(func, x0[, fprime, args, ...])	Minimize a function with variables subject to bounds, using
fmin_cobyla(func, x0, cons[, args, ...])	Minimize a function using the Constrained Optimization BY Linear
fmin_slsqp(func, x0[, eqcons, f_eqcons, ...])	Minimize a function using Sequential Least SQuares Programming
nnls(A, b)	Solve argmin_x || Ax - b ||_2 for x>=0. This is a wrapper

Global

anneal(func, x0[, args, schedule, ...])	Minimize a function using simulated annealing.
basinhopping(func, x0[, niter, T, stepsize, ...])	Find the global minimum of a function using the basin-hopping algorithm ..
brute(func, ranges[, args, Ns, full_output, ...])	Minimize a function over a given range by brute force.

Scalar function minimizers

minimize_scalar(fun[, bracket, bounds, ...])	Minimization of scalar function of one variable.
fminbound(func, x1, x2[, args, xtol, ...])	Bounded minimization for scalar functions.
brent(func[, args, brack, tol, full_output, ...])	Given a function of one-variable and a possible bracketing interval, return the minimum of the function isolated to a fractional precision of tol.
golden(func[, args, brack, tol, full_output])	Return the minimum of a function of one variable.
bracket(func[, xa, xb, args, grow_limit, ...])	Bracket the minimum of the function.

Rosenbrock function

rosen(x)	The Rosenbrock function.
rosen_der(x)	The derivative (i.e.
rosen_hess(x)	The Hessian matrix of the Rosenbrock function.
rosen_hess_prod(x, p)	Product of the Hessian matrix of the Rosenbrock function with a vector.

Fitting

curve_fit(f, xdata, ydata[, p0, sigma])

Use non-linear least squares to fit a function, f, to data.

Root finding

Scalar functions

brentq(f, a, b[, args, xtol, rtol, maxiter, ...])	Find a root of a function in given interval.
brenth(f, a, b[, args, xtol, rtol, maxiter, ...])	Find root of f in [a,b].
ridder(f, a, b[, args, xtol, rtol, maxiter, ...])	Find a root of a function in an interval.
bisect(f, a, b[, args, xtol, rtol, maxiter, ...])	Find root of a function within an interval.
newton(func, x0[, fprime, args, tol, ...])	Find a zero using the Newton-Raphson or secant method.

Fixed point finding:

fixed_point(func, x0[, args, xtol, maxiter])

Find a fixed point of the function.

Multidimensional

General nonlinear solvers:

root(fun, x0[, args, method, jac, tol, ...])	Find a root of a vector function.
fsolve(func, x0[, args, fprime, ...])	Find the roots of a function.
broyden1(F, xin[, iter, alpha, ...])	Find a root of a function, using Broyden’s first Jacobian approximation.
broyden2(F, xin[, iter, alpha, ...])	Find a root of a function, using Broyden’s second Jacobian approximation.

Large-scale nonlinear solvers:

newton_krylov(F, xin[, iter, rdiff, method, ...])	Find a root of a function, using Krylov approximation for inverse Jacobian.
anderson(F, xin[, iter, alpha, w0, M, ...])	Find a root of a function, using (extended) Anderson mixing.

Simple iterations:

excitingmixing(F, xin[, iter, alpha, ...])	Find a root of a function, using a tuned diagonal Jacobian approximation.
linearmixing(F, xin[, iter, alpha, verbose, ...])	Find a root of a function, using a scalar Jacobian approximation.
diagbroyden(F, xin[, iter, alpha, verbose, ...])	Find a root of a function, using diagonal Broyden Jacobian approximation.

Additional information on the nonlinear solvers

Utility Functions

line_search(f, myfprime, xk, pk[, gfk, ...])	Find alpha that satisfies strong Wolfe conditions.
check_grad(func, grad, x0, *args)	Check the correctness of a gradient function by comparing it against a (forward) finite-difference approximation of the gradient.
show_options(solver[, method])	Show documentation for additional options of optimization solvers.