SciPy

scipy.optimize.fmin_slsqp

scipy.optimize.fmin_slsqp(func, x0, eqcons=(), f_eqcons=None, ieqcons=(), f_ieqcons=None, bounds=(), fprime=None, fprime_eqcons=None, fprime_ieqcons=None, args=(), iter=100, acc=1e-06, iprint=1, disp=None, full_output=0, epsilon=1.4901161193847656e-08, callback=None)[source]

Minimize a function using Sequential Least SQuares Programming

Python interface function for the SLSQP Optimization subroutine originally implemented by Dieter Kraft.

Parameters :

func : callable f(x,*args)

Objective function.

x0 : 1-D ndarray of float

Initial guess for the independent variable(s).

eqcons : list

A list of functions of length n such that eqcons[j](x,*args) == 0.0 in a successfully optimized problem.

f_eqcons : callable f(x,*args)

Returns a 1-D array in which each element must equal 0.0 in a successfully optimized problem. If f_eqcons is specified, eqcons is ignored.

ieqcons : list

A list of functions of length n such that ieqcons[j](x,*args) >= 0.0 in a successfully optimized problem.

f_ieqcons : callable f(x,*args)

Returns a 1-D ndarray in which each element must be greater or equal to 0.0 in a successfully optimized problem. If f_ieqcons is specified, ieqcons is ignored.

bounds : list

A list of tuples specifying the lower and upper bound for each independent variable [(xl0, xu0),(xl1, xu1),...] Infinite values will be interpreted as large floating values.

fprime : callable f(x,*args)

A function that evaluates the partial derivatives of func.

fprime_eqcons : callable f(x,*args)

A function of the form f(x, *args) that returns the m by n array of equality constraint normals. If not provided, the normals will be approximated. The array returned by fprime_eqcons should be sized as ( len(eqcons), len(x0) ).

fprime_ieqcons : callable f(x,*args)

A function of the form f(x, *args) that returns the m by n array of inequality constraint normals. If not provided, the normals will be approximated. The array returned by fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ).

args : sequence

Additional arguments passed to func and fprime.

iter : int

The maximum number of iterations.

acc : float

Requested accuracy.

iprint : int

The verbosity of fmin_slsqp :

  • iprint <= 0 : Silent operation
  • iprint == 1 : Print summary upon completion (default)
  • iprint >= 2 : Print status of each iterate and summary

disp : int

Over-rides the iprint interface (preferred).

full_output : bool

If False, return only the minimizer of func (default). Otherwise, output final objective function and summary information.

epsilon : float

The step size for finite-difference derivative estimates.

callback : callable, optional

Called after each iteration, as callback(x), where x is the current parameter vector.

Returns :

out : ndarray of float

The final minimizer of func.

fx : ndarray of float, if full_output is true

The final value of the objective function.

its : int, if full_output is true

The number of iterations.

imode : int, if full_output is true

The exit mode from the optimizer (see below).

smode : string, if full_output is true

Message describing the exit mode from the optimizer.

See also

minimize
Interface to minimization algorithms for multivariate functions. See the ‘SLSQP’ method in particular.

Notes

Exit modes are defined as follows

-1 : Gradient evaluation required (g & a)
 0 : Optimization terminated successfully.
 1 : Function evaluation required (f & c)
 2 : More equality constraints than independent variables
 3 : More than 3*n iterations in LSQ subproblem
 4 : Inequality constraints incompatible
 5 : Singular matrix E in LSQ subproblem
 6 : Singular matrix C in LSQ subproblem
 7 : Rank-deficient equality constraint subproblem HFTI
 8 : Positive directional derivative for linesearch
 9 : Iteration limit exceeded

Examples

Examples are given in the tutorial.