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)

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),...]

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.

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.

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.