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""" ===================================================== Optimization and root finding (:mod:`scipy.optimize`) =====================================================
.. currentmodule:: scipy.optimize
Optimization ============
Local Optimization ------------------
.. autosummary:: :toctree: generated/
minimize - Interface for minimizers of multivariate functions minimize_scalar - Interface for minimizers of univariate functions OptimizeResult - The optimization result returned by some optimizers OptimizeWarning - The optimization encountered problems
The `minimize` function supports the following methods:
.. toctree::
optimize.minimize-neldermead optimize.minimize-powell optimize.minimize-cg optimize.minimize-bfgs optimize.minimize-newtoncg optimize.minimize-lbfgsb optimize.minimize-tnc optimize.minimize-cobyla optimize.minimize-slsqp optimize.minimize-trustconstr optimize.minimize-dogleg optimize.minimize-trustncg optimize.minimize-trustkrylov optimize.minimize-trustexact
Constraints are passed to `minimize` function as a single object or as a list of objects from the following classes:
.. autosummary:: :toctree: generated/
NonlinearConstraint - Class defining general nonlinear constraints. LinearConstraint - Class defining general linear constraints.
Simple bound constraints are handled separately and there is a special class for them:
.. autosummary:: :toctree: generated/
Bounds - Bound constraints.
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:
.. autosummary:: :toctree: generated/
BFGS - Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy. SR1 - Symmetric-rank-1 Hessian update strategy.
The `minimize_scalar` function supports the following methods:
.. toctree::
optimize.minimize_scalar-brent optimize.minimize_scalar-bounded optimize.minimize_scalar-golden
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:
.. autosummary:: :toctree: generated/
fmin - Nelder-Mead Simplex algorithm fmin_powell - Powell's (modified) level set method fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno) fmin_ncg - Line-search Newton Conjugate Gradient
Constrained multivariate methods:
.. autosummary:: :toctree: generated/
fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer fmin_tnc - Truncated Newton code fmin_cobyla - Constrained optimization by linear approximation fmin_slsqp - Minimization using sequential least-squares programming differential_evolution - stochastic minimization using differential evolution
Univariate (scalar) minimization methods:
.. autosummary:: :toctree: generated/
fminbound - Bounded minimization of a scalar function brent - 1-D function minimization using Brent method golden - 1-D function minimization using Golden Section method
Equation (Local) Minimizers ---------------------------
.. autosummary:: :toctree: generated/
leastsq - Minimize the sum of squares of M equations in N unknowns least_squares - Feature-rich least-squares minimization. nnls - Linear least-squares problem with non-negativity constraint lsq_linear - Linear least-squares problem with bound constraints
Global Optimization -------------------
.. autosummary:: :toctree: generated/
basinhopping - Basinhopping stochastic optimizer brute - Brute force searching optimizer differential_evolution - stochastic minimization using differential evolution
Rosenbrock function -------------------
.. autosummary:: :toctree: generated/
rosen - The Rosenbrock function. rosen_der - The derivative of the Rosenbrock function. rosen_hess - The Hessian matrix of the Rosenbrock function. rosen_hess_prod - Product of the Rosenbrock Hessian with a vector.
Fitting =======
.. autosummary:: :toctree: generated/
curve_fit -- Fit curve to a set of points
Root finding ============
Scalar functions ---------------- .. autosummary:: :toctree: generated/
brentq - quadratic interpolation Brent method brenth - Brent method, modified by Harris with hyperbolic extrapolation ridder - Ridder's method bisect - Bisection method newton - Secant method or Newton's method
Fixed point finding:
.. autosummary:: :toctree: generated/
fixed_point - Single-variable fixed-point solver
Multidimensional ----------------
General nonlinear solvers:
.. autosummary:: :toctree: generated/
root - Unified interface for nonlinear solvers of multivariate functions fsolve - Non-linear multi-variable equation solver broyden1 - Broyden's first method broyden2 - Broyden's second method
The `root` function supports the following methods:
.. toctree::
optimize.root-hybr optimize.root-lm optimize.root-broyden1 optimize.root-broyden2 optimize.root-anderson optimize.root-linearmixing optimize.root-diagbroyden optimize.root-excitingmixing optimize.root-krylov optimize.root-dfsane
Large-scale nonlinear solvers:
.. autosummary:: :toctree: generated/
newton_krylov anderson
Simple iterations:
.. autosummary:: :toctree: generated/
excitingmixing linearmixing diagbroyden
:mod:`Additional information on the nonlinear solvers <scipy.optimize.nonlin>`
Linear Programming ==================
General linear programming solver:
.. autosummary:: :toctree: generated/
linprog -- Unified interface for minimizers of linear programming problems
The `linprog` function supports the following methods:
.. toctree::
optimize.linprog-simplex optimize.linprog-interior-point
The simplex method supports callback functions, such as:
.. autosummary:: :toctree: generated/
linprog_verbose_callback -- Sample callback function for linprog (simplex)
Assignment problems:
.. autosummary:: :toctree: generated/
linear_sum_assignment -- Solves the linear-sum assignment problem
Utilities =========
.. autosummary:: :toctree: generated/
approx_fprime - Approximate the gradient of a scalar function bracket - Bracket a minimum, given two starting points check_grad - Check the supplied derivative using finite differences line_search - Return a step that satisfies the strong Wolfe conditions
show_options - Show specific options optimization solvers LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian HessianUpdateStrategy - Interface for implementing Hessian update strategies
"""
LinearConstraint, Bounds)
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