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SciPy Reference Guide, Release 0.8.dev func – Function to be optimized x0 – Parameters to be optimized over args – Extra parameters to function schedule – Annealing schedule to use (a class) full_output – Return optional outputs T0 – Initial Temperature (estimated as 1.2 times the largest cost-function deviation over random points in the range) Tf – Final goal temperature maxeval – Maximum function evaluations maxaccept – Maximum changes to accept maxiter – Maximum cooling iterations learn_rate – scale constant for adjusting guesses boltzmann – Boltzmann constant in acceptance test (increase for less stringent test at each temperature). feps – Stopping relative error tolerance for the function value in last four coolings. quench, m, n – Parameters to alter fast_sa schedule lower, upper – lower and upper bounds on x0 (scalar or array). dwell – The number of times to search the space at each temperature. Outputs: (xmin, {Jmin, T, feval, iters, accept,} retval) xmin – Point giving smallest value found retval – Flag indicating stopping condition: 0 : Cooled to global optimum 1 : Cooled to final temperature 2 : Maximum function evaluations 3 : Maximum cooling iterations reached 4 : Maximum accepted query locations reached Jmin – Minimum value of function found T – final temperature feval – Number of function evaluations iters – Number of cooling iterations accept – Number of tests accepted. See also: fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg – multivariate local optimizers leastsq – nonlinear least squares minimizer fmin_l_bfgs_b, fmin_tnc, fmin_cobyla – constrained multivariate optimizers anneal, brute – global optimizers fminbound, brent, golden, bracket – local scalar minimizers fsolve – n-dimensional root-finding brentq, brenth, ridder, bisect, newton – one-dimensional root-finding fixed_point – scalar fixed-point finder OpenOpt – Python package with more optimization solvers brute(func, ranges, args=(), Ns=20, full_output=0, finish=) Minimize a function over a given range by brute force. Parameters func [callable f(x,*args)] Objective function to be minimized. ranges [tuple] Each element is a tuple of parameters or a slice object to be handed to numpy.mgrid. args [tuple] Extra arguments passed to function. 312 Chapter 3. Reference
Ns [int] Default number of samples, if those are not provided. full_output [bool] If True, return the evaluation grid. Returns (x0, fval, {grid, Jout}) x0 [ndarray] Value of arguments to func, giving minimum over the grid. fval [int] Function value at minimum. SciPy Reference Guide, Release 0.8.dev grid [tuple] Representation of the evaluation grid. It has the same length as x0. Jout [ndarray] Function values over grid: Jout = func(*grid). Notes Find the minimum of a function evaluated on a grid given by the tuple ranges. Scalar function minimizers fminbound(func, x1, x2[, args, xtol, ...]) golden(func[, args, brack, tol, full_output]) bracket(func[, xa, xb, args, grow_limit, ...]) brent(func[, args, brack, tol, full_output, ...]) Bounded minimization for scalar functions. Given a function of one-variable and a possible bracketing interval, return the minimum of the function isolated to a fractional precision of tol. Given a function and distinct initial points, search in the downhill direction (as defined by the initital points) and return new points xa, xb, xc that bracket the minimum of the function f(xa) > f(xb) < f(xc). Given a function of one-variable and a possible bracketing interval, return the minimum of the function isolated to a fractional precision of tol. fminbound(func, x1, x2, args=(), xtol=1.0000000000000001e-05, maxfun=500, full_output=0, disp=1) Bounded minimization for scalar functions. Parameters func [callable f(x,*args)] Objective function to be minimized (must accept and return scalars). x1, x2 [float or array scalar] The optimization bounds. args [tuple] Extra arguments passed to function. xtol [float] The convergence tolerance. maxfun [int] Maximum number of function evaluations allowed. full_output [bool] If True, return optional outputs. 3.12. Optimization and root finding (<strong>scipy</strong>.optimize) 313
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