Optimization and root finding (scipy.optimize)


Local Optimization

minimize(fun, x0[, args, method, jac, hess, ...]) Minimization of scalar function of one or more variables.
minimize_scalar(fun[, bracket, bounds, ...]) Minimization of scalar function of one variable.
OptimizeResult Represents the optimization result.

The specific optimization method interfaces below in this subsection are not recommended for use in new scripts; all of these methods are accessible via a newer, more consistent interface provided by the functions above.

General-purpose multivariate methods:

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.
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.

Constrained multivariate methods:

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 gradient information in a truncated Newton algorithm.
fmin_cobyla(func, x0, cons[, args, ...]) Minimize a function using the Constrained Optimization BY Linear Approximation (COBYLA) method.
fmin_slsqp(func, x0[, eqcons, f_eqcons, ...]) Minimize a function using Sequential Least SQuares Programming

Univariate (scalar) minimization methods:

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.

Equation (Local) Minimizers

leastsq(func, x0[, args, Dfun, full_output, ...]) Minimize the sum of squares of a set of equations.
nnls(A, b) Solve argmin_x || Ax - b ||_2 for x>=0.

Global Optimization

anneal(*args, **kwds) anneal is deprecated!
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.

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.


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.


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

approx_fprime(xk, f, epsilon, *args) Finite-difference approximation of the gradient of a scalar function.
bracket(func[, xa, xb, args, grow_limit, ...]) Bracket the minimum of the function.
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.
line_search(f, myfprime, xk, pk[, gfk, ...]) Find alpha that satisfies strong Wolfe conditions.
show_options([solver, method]) Show documentation for additional options of optimization solvers.