loupe.optimize#

loupe.optimize(fun, params, ftol=1e-09, gtol=1e-05, maxiter=1000, analytic_grad=True)[source]#

Minimize a scalar function of one or more variables using the L-BFGS-B algorithm.

This function constructs a call to scipy.optimize.minimize() with method = ‘L-BFGS-B’.

Parameters:

  • fun (Function) – The objective function to be minimized.

  • params (list of array or array) – Parameters in fun to optimize.

  • ftol (float, optional) – Termination tolerance on the objective function value. Default is 1e-9.

  • gtol (float, optional) – Termination tolerance on the gradient value. Default is 1e-6.

  • maxiter (int, optional) – Maximum number of iterations. Default is 1000.

  • analytic_grad (bool, optional) – If true (default), the gradient vector is analytically computed using algorithmic differentiation. If false, the gradient is numerically estimated by a finite difference algorithm.

Returns:

res – The optimization result. Important attributes are: x the solution array, success a Boolean flag indicating if the optimizer exited successfully and message which describes the cause of the termination. See OptimizeResult for a full description of other attributes.

Return type:

OptimizeResult

Examples

Construct a simple quadratic objective function and compute the minimum value of x:

>>> x = loupe.rand()
>>> y = 4*(x-5)**2
>>> loupe.optimize(y, params=x)

     fun: array(1.26217745e-29)
hess_inv: <1x1 LbfgsInvHessProduct with dtype=float64>
     jac: array([-1.42108547e-14])
 message: 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'
    nfev: 3
     nit: 2
    njev: 3
  status: 0
 success: True
       x: array([5.])

Optimize the same function, this time using the finite difference gradient:

>>> x = loupe.rand()
>>> y = 4*(x-5)**2
>>> loupe.optimize(y, params=x, analytic_grad=False)

     fun: array(8.4112054e-13)
hess_inv: <1x1 LbfgsInvHessProduct with dtype=float64>
     jac: array([3.70850496e-06])
 message: 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'
    nfev: 6
     nit: 2
    njev: 3
  status: 0
 success: True
       x: array([5.00000046])
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