Optimization and root finding (scipy.optimize)¶
Optimization¶
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. |
| OptimizeWarning |
The minimize function supports the following methods:
The minimize_scalar function supports the following methods:
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 |
| differential_evolution(func, bounds[, args, ...]) | Finds the global minimum of a multivariate function. |
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, ...]) | 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. |
| least_squares(fun, x0[, jac, bounds, ...]) | Solve a nonlinear least-squares problem with bounds on the variables. |
| nnls(A, b) | Solve argmin_x || Ax - b ||_2 for x>=0. |
| lsq_linear(A, b[, bounds, method, tol, ...]) | Solve a linear least-squares problem with bounds on the variables. |
Global Optimization¶
| 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. |
| differential_evolution(func, bounds[, args, ...]) | Finds the global minimum of a multivariate 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 a bracketing interval using Brent’s method. |
| 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. |
The root function supports the following methods:
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. |
Linear Programming¶
Simplex Algorithm:
| linprog(c[, A_ub, b_ub, A_eq, b_eq, bounds, ...]) | Minimize a linear objective function subject to linear equality and inequality constraints. |
| linprog_verbose_callback(xk, **kwargs) | A sample callback function demonstrating the linprog callback interface. |
The linprog function supports the following methods:
Assignment problems:
| linear_sum_assignment(cost_matrix) | Solve the linear sum assignment problem. |
Utilities¶
| 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, **kwargs) | 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, disp]) | Show documentation for additional options of optimization solvers. |
| LbfgsInvHessProduct(sk, yk) | Linear operator for the L-BFGS approximate inverse Hessian. |