Python SOLNP (pysolnp)

pysolnp provides Python with the power of the SOLNP algorithm explained in Introduction section. It is simply a Python wrapper for C++ solnp.

Installation

In most situations, installing with the package installer for Python, pip, will work:

$ pip install pysolnp

Precompiled Wheels are available for CPython:

Windows: Python 3.6+
Linux: Python 3.6+
Mac OS: Python 3.6+

For other systems, or to have BLAS and LAPACK support, please build the wheels manually.

$ pip install --no-binary :all: pysolnp

Note that this requires CMake.

Method

solve(obj_func: function,
      par_start_value: List,
      par_lower_limit: object = None,
      par_upper_limit: object = None,
      eq_func: object = None,
      eq_values: object = None,
      ineq_func: object = None,
      ineq_lower_bounds: object = None,
      ineq_upper_bounds: object = None,
      rho: float = 1.0,
      max_major_iter: int = 10,
      max_minor_iter: int = 10,
      delta: float = 1e-05,
      tolerance: float = 0.0001,
      debug: bool = False) -> pysolnp.Result

Inputs

Parameter	Type	Default value 1	Description
obj_func	Callable[List, float]		The objective function $f(x)$ to minimize.
par_start_value	List		The starting parameter $x_0$ .
par_lower_limit	List	None	The parameter lower limit $x_l$ .
par_upper_limit	List	None	The parameter upper limit $x_u$ .
eq_func	Callable[List, float]	None	The equality constraint function $h(x)$ .
eq_values	List	None	The equality constraint values $e_x$ .
ineq_func	Callable[List, float]	None	The inequality constraint function $g(x)$ .
ineq_lower_bounds	List	None	The inequality constraint lower limit $g_l$ .
ineq_upper_bounds	List	None	The inequality constraint upper limit $g_l$ .
rho	float	1.0	Penalty weighting scalar for infeasability in the augmented objective function. 2
max_major_iter	int	400	Maximum number of outer iterations.
max_minor_iter	int	800	Maximum number of inner iterations.
delta	float	1e-07	Step-size for forward differentiation.
tolerance	float	1e-08	Relative tolerance on optimality.
debug	bool	False	If set to true some debug output will be printed.

1: Defaults for configuration parameters are based on the defaults for Rsolnp.
2: Higher values means the solution will bring the solution into the feasible region with higher weight. Very high values might lead to numerical ill conditioning or slow down convergence.

Outputs

The function returns the pysolnp.Result object with the below properties.

Property	Type	Description
solve_value	float	The value of the objective function at optimum $f(x*)$ .
optimum	List[float]	A list of parameters for the optimum $x*$ .
callbacks	int	Number of callbacks done to find this optimum.
converged	boolean	Indicates if the algorithm converged or not.
hessian_matrix	List[List[float]]	The final Hessian Matrix used by pysolnp.

Example 1: Box Problem

The Box Problem is a common example function used for testing optimization algorithms. It has one equality constraint and variable bounds.

import pysolnp

def f_objective_function(x):
    return -1 * x[0] * x[1] * x[2]

def g_equality_constraint_function(x):
    return [4 * x[0] * x[1] + 2 * x[1] * x[2] + 2 * x[2] * x[0]]

x_starting_point = [1.1, 1.1, 9.0]
x_l = [1.0, 1.0, 1.0]
x_u = [10.0, 10.0, 10.0]
e_x = [100]

result = pysolnp.solve(
    obj_func=f_objective_function,
    par_start_value=x_starting_point,
    par_lower_limit=x_l,
    par_upper_limit=x_u,
    eq_func=g_equality_constraint_function,
    eq_values=e_x)

result.solve_value
result.optimum
result.callbacks
result.converged

Running this will yield the output:

>>> result.solve_value
-48.11252206814995
>>> result.optimum
[2.8867750707815447, 2.8867750713194273, 5.773407748939196]
>>> result.callbacks
118
>>> result.converged
True

Use-cases and Applications

NMPC - Nonlinear model predictive controls-case studies using Matlab, REXYGEN and pysolnp NLP solver under Python environment by Štěpán Ožana. [NMPC Overhead Crane (PDF)] [GitHub Source Code] [Štěpán’s Homepage]