pyglobalsearch.PyProblem

class pyglobalsearch.PyProblem(objective, variable_bounds, gradient=None, hessian=None, constraints=None)

Bases: object

Defines an optimization problem to be solved.

A PyProblem encapsulates all the mathematical components needed for optimization: the objective function to minimize, variable bounds, and optional gradient, Hessian, and constraint functions.

Parameters:

• objective (callable) – Function that takes x (array-like) and returns the value to minimize (float)

• variable_bounds (callable) – Function that returns bounds array of shape (n_vars, 2) with [lower, upper] bounds

• gradient (callable, optional) – Function that takes x and returns gradient array (for gradient-based solvers)

• hessian (callable, optional) – Function that takes x and returns Hessian matrix (for Newton-type solvers)

• constraints (list[callable], optional) – List of constraint functions where constraint(x) >= 0 means satisfied

Examples

Basic unconstrained problem:

>>> def objective(x): return x[0]**2 + x[1]**2
>>> def bounds(): return np.array([[-5, 5], [-5, 5]])
>>> problem = gs.PyProblem(objective, bounds)

Problem with gradient for faster convergence:

>>> def gradient(x): return np.array([2*x[0], 2*x[1]])
>>> problem = gs.PyProblem(objective, bounds, gradient=gradient)

Constrained problem (requires COBYLA solver):

>>> def constraint(x): return x[0] + x[1] - 1  # x[0] + x[1] >= 1
>>> problem = gs.PyProblem(objective, bounds, constraints=[constraint])

__init__()

Methods

__init__()

Attributes

constraints	List of constraint functions
gradient	Function returning the gradient
hessian	Function returning the Hessian matrix
objective	Objective function to minimize
variable_bounds	Function returning variable bounds

constraints

List of constraint functions

Parameters:

x – Input parameters as a list or array of floats

Returns:

Constraint value (float), should be >= 0 to be satisfied

Raises:

ValueError – If any constraint function does not return a float

gradient

Function returning the gradient

Parameters:

x – Input parameters as a list or array of floats

Returns:

Gradient as a list or array of floats

Raises:

ValueError – If the gradient length does not match the number of variables

hessian

Function returning the Hessian matrix

Parameters:

x – Input parameters as a list or array of floats

Returns:

Hessian matrix as a 2D list or array of floats

Raises:

ValueError – If the Hessian is not square or does not match the number of variables

objective

Objective function to minimize

Parameters:

x – Input parameters as a list or array of floats

Returns:

Objective function value (float)

variable_bounds

Function returning variable bounds

Returns:

2D array-like of shape (n_vars, 2) with [lower, upper] bounds for each variable

Return type:

array-like