Subroutine Type

Utility/Data Access

Definition

SLSQP optimizer is a sequential least squares programming algorithm for nonlinear, constrained gradient-based optimization.  It supports both inequality and equality constraints.

Note: FMIN_SLQP is only available as a Python function.

This function is also documented in Scipy at scipy.optimize.fmin_slsqp.

Use

The utility can be called by any user-defined subroutine written in Python.

Calling Syntax

Python

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)

Input Arguments

func

A function that can be called by Python that evaluates the objective function that is to be minimized.

Type: Callable function of the form f(x, *args)

X0

The initial guess for the independent variables.

Type: A 1-D array of floats.  Denote N = len(x0)

eqcons

A list of functions of length N that specify all the equality constraints that FMIN_SLSQP must maintain.  In a successfully optimized problem, FMIN_SLSQP will ensure that eqcons[i](x,*args) == 0, i=1…M, where M=len(eqcons)

Type: List

f_eqcons

f_eqcons is a function that can be called by Python.  This function returns a 1-D array of floats that must equal 0.0 in a successfully optimized problem. F_eqcons has the form: f(x, *args)

If eqcons is specpfied, f_eqcons is ignored.

Type: Callable function of the form f(x, *args)

ieqcons

A list of functions of length N that specify all the inequality constraints that FMIN_SLSQP must satisfy.  In a successfully optimized problem, FMIN_SLSQP will ensure that ieqcons[i](x,*args) >= 0, i=1…M’, where M’=len(ieqcons)

Type: List

f_ieqcons

f_ieqcons is a function that can be called by Python.  This function returns a 1-D array of floats that must be greater than or equal 0.0 in a successfully optimized problem.

F_eqcons has the form: f(x, *args)

If ieqcons is specified, f_ieqcons is ignored.

Type: Callable function of the form f(x, *args)

bounds

A list of types specifying the lower and upper bound for each independent variable.  It has the form:
[ (xl0,xu0), (xl1,xu1), ... (xlN,xuN)]

Type: Callable function of the form f(x, *args)

fprime

A function that evaluates the partial derivatives of func with respect to the independent variables.

Type: Callable function of the form f(x, *args) that returns a 1-D array of length N.

fprime_eqcons

A function that can be called by Python. This function returns the Jacobian matrix of the equality constraints in an M x N array of floats.

If fprime_eqcons is not provided, the Jacobian matrix is obtained through finite differencing.  Finite differencing can be expensive and is known to be sometimes inaccurate.

Type: Callable function of the form f(x, *args) that returns an M x N array.

fprime_ieqcons

A function that can be called by Python.  This function returns the Jacobian matrix of the equality constraints in an M’ x N array of floats.

If fprime_ieqcons is not provided, the Jacobian matrix is obtained through finite differencing.  Finite differencing can be expensive and is known to be sometimes inaccurate.

Type: Callable function of the form f(x, *args) that returns an M’ x N array.

args

These are the additional arguments that are passed to func, fprime, fprime_eqcons and fprime_ieqcons

Type: Sequence

iter

This specifies the maximum number of iterations available to FMIN_SLSQP to obtain a minimum.

Type: Integer

acc

This is the accuracy to which a solution is desired.

Type: Float

iprint

This defines the verbosity of the diagnostics generated by FMIN_SLSQP.

Type = integer

disp

This defines the verbosity of the diagnostics generated by FMIN_SLSQP. When specified, disp overrides the iprint interface.

Type = integer

full_output

If false, it returns only the minimizer of func (default).  Otherwise, it returns the output final objective function and summary information.

Type = bool

epsilon

The step size for finite-difference derivative estimates.

Type = float

Output Values

out

The final minimizer of func.

Type: 1-D float array

fx

If full_output is true, fx will contain the final value of the objective function.

Type: 1-D float array

its

If full_output is true, this will contain the number of iterations taken.

Type = int

imode

If full_output is true, this will contain the exit mode from the optimizer.  The values of imode have the following significance:

-1: Gradient evaluation required

0: Optimization terminated successfully.

1: Function evaluation required

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

Type = int

smode

If full_output is true, this will contain a message describing the exit mode from the optimizer.

Type = string

Comments

FMIN_SLSQP is the interface function for the SLSQP optimization function originally implemented by Dieter Kraft.  SLSQP is a Sequential, Least SQuares Programming algorithm.

Optimization can be done in MotionSolve through the use of a CONSUB user subroutine together with FMIN_SLSQP.  This can be used for model identification or mechanism optimization.  The CONSUB may be written in Fortran/C/C++ or Python/MATLAB scripts.