optimize.slsqp

This module implements the Sequential Least SQuares Programming optimization algorithm (SLSQP), originally developed by Dieter Kraft. See http://www.netlib.org/toms/733

Module Contents

Functions

approx_jacobian(x,func,epsilon,*args) Approximate the Jacobian matrix of a callable function.
fmin_slsqp(func,x0,eqcons=tuple,f_eqcons=None,ieqcons=tuple,f_ieqcons=None,bounds=tuple,fprime=None,fprime_eqcons=None,fprime_ieqcons=None,args=tuple,iter=100,acc=1e-06,iprint=1,disp=None,full_output=0,epsilon=_epsilon,callback=None) Minimize a function using Sequential Least SQuares Programming
_minimize_slsqp(func,x0,args=tuple,jac=None,bounds=None,constraints=tuple,maxiter=100,ftol=1e-06,iprint=1,disp=False,eps=_epsilon,callback=None,**unknown_options) Minimize a scalar function of one or more variables using Sequential
fun(x,r=list) Objective function
feqcon(x,b=1) Equality constraint
jeqcon(x,b=1) Jacobian of equality constraint
fieqcon(x,c=10) Inequality constraint
jieqcon(x,c=10) Jacobian of Inequality constraint
approx_jacobian(x, func, epsilon, *args)

Approximate the Jacobian matrix of a callable function.

x : array_like
The state vector at which to compute the Jacobian matrix.
func : callable f(x,*args)
The vector-valued function.
epsilon : float
The perturbation used to determine the partial derivatives.
args : sequence
Additional arguments passed to func.

An array of dimensions (lenf, lenx) where lenf is the length of the outputs of func, and lenx is the number of elements in x.

The approximation is done using forward differences.

fmin_slsqp(func, x0, eqcons=tuple, f_eqcons=None, ieqcons=tuple, f_ieqcons=None, bounds=tuple, fprime=None, fprime_eqcons=None, fprime_ieqcons=None, args=tuple, iter=100, acc=1e-06, iprint=1, disp=None, full_output=0, epsilon=_epsilon, callback=None)

Minimize a function using Sequential Least SQuares Programming

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

func : callable f(x,*args)
Objective function. Must return a scalar.
x0 : 1-D ndarray of float
Initial guess for the independent variable(s).
eqcons : list, optional
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), optional
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, optional
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), optional
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, optional
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), optional
A function that evaluates the partial derivatives of func.
fprime_eqcons : callable f(x,*args), optional
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), optional
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, optional
Additional arguments passed to func and fprime.
iter : int, optional
The maximum number of iterations.
acc : float, optional
Requested accuracy.
iprint : int, optional

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, optional
Over-rides the iprint interface (preferred).
full_output : bool, optional
If False, return only the minimizer of func (default). Otherwise, output final objective function and summary information.
epsilon : float, optional
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.
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.
minimize: Interface to minimization algorithms for multivariate
functions. See the ‘SLSQP’ method in particular.

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 are given in the tutorial.

_minimize_slsqp(func, x0, args=tuple, jac=None, bounds=None, constraints=tuple, maxiter=100, ftol=1e-06, iprint=1, disp=False, eps=_epsilon, callback=None, **unknown_options)

Minimize a scalar function of one or more variables using Sequential Least SQuares Programming (SLSQP).

ftol : float
Precision goal for the value of f in the stopping criterion.
eps : float
Step size used for numerical approximation of the Jacobian.
disp : bool
Set to True to print convergence messages. If False, verbosity is ignored and set to 0.
maxiter : int
Maximum number of iterations.
fun(x, r=list)

Objective function

feqcon(x, b=1)

Equality constraint

jeqcon(x, b=1)

Jacobian of equality constraint

fieqcon(x, c=10)

Inequality constraint

jieqcon(x, c=10)

Jacobian of Inequality constraint