Optimization and root finding ( scipy.optimize )#
SciPy optimize provides functions for minimizing (or maximizing) objective functions, possibly subject to constraints. It includes solvers for nonlinear problems (with support for both local and global optimization algorithms), linear programing, constrained and nonlinear least-squares, root finding, and curve fitting.
Common functions and objects, shared across different solvers, are:
Show documentation for additional options of optimization solvers.
Represents the optimization result.
Optimization#
Scalar functions optimization#
Minimization of scalar function of one variable.
The minimize_scalar function supports the following methods:
Local (multivariate) optimization#
minimize (fun, x0[, args, method, jac, hess, . ])
Minimization of scalar function of one or more variables.
The minimize function supports the following methods:
- minimize(method=’Nelder-Mead’)
- minimize(method=’Powell’)
- minimize(method=’CG’)
- minimize(method=’BFGS’)
- minimize(method=’Newton-CG’)
- minimize(method=’L-BFGS-B’)
- minimize(method=’TNC’)
- minimize(method=’COBYLA’)
- minimize(method=’SLSQP’)
- minimize(method=’trust-constr’)
- minimize(method=’dogleg’)
- minimize(method=’trust-ncg’)
- minimize(method=’trust-krylov’)
- minimize(method=’trust-exact’)
Constraints are passed to minimize function as a single object or as a list of objects from the following classes:
Nonlinear constraint on the variables.
Linear constraint on the variables.
Simple bound constraints are handled separately and there is a special class for them:
Bounds constraint on the variables.
Quasi-Newton strategies implementing HessianUpdateStrategy interface can be used to approximate the Hessian in minimize function (available only for the ‘trust-constr’ method). Available quasi-Newton methods implementing this interface are:
Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
Symmetric-rank-1 Hessian update strategy.
Global optimization#
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.
Finds the global minimum of a multivariate function.
shgo (func, bounds[, args, constraints, n, . ])
Finds the global minimum of a function using SHG optimization.
Find the global minimum of a function using Dual Annealing.
direct (func, bounds, *[, args, eps, maxfun, . ])
Finds the global minimum of a function using the DIRECT algorithm.
Least-squares and curve fitting#
Nonlinear least-squares#
Solve a nonlinear least-squares problem with bounds on the variables.
Linear least-squares#
Solve argmin_x || Ax — b ||_2 for x>=0 .
Solve a linear least-squares problem with bounds on the variables.
Curve fitting#
Use non-linear least squares to fit a function, f, to data.
Root finding#
Scalar functions#
Find a root of a scalar function.
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 a root of a function in a bracketing interval using Brent’s method with hyperbolic extrapolation.
ridder (f, a, b[, args, xtol, rtol, maxiter, . ])
Find a root of a function in an interval using Ridder’s method.
bisect (f, a, b[, args, xtol, rtol, maxiter, . ])
Find root of a function within an interval using bisection.
Find a root of a real or complex function using the Newton-Raphson (or secant or Halley’s) method.
Find a root using TOMS Algorithm 748 method.
Represents the root finding result.
The root_scalar function supports the following methods:
The table below lists situations and appropriate methods, along with asymptotic convergence rates per iteration (and per function evaluation) for successful convergence to a simple root(*). Bisection is the slowest of them all, adding one bit of accuracy for each function evaluation, but is guaranteed to converge. The other bracketing methods all (eventually) increase the number of accurate bits by about 50% for every function evaluation. The derivative-based methods, all built on newton , can converge quite quickly if the initial value is close to the root. They can also be applied to functions defined on (a subset of) the complex plane.