gemseo.problems.optimization.power_2 module#

A quadratic analytical problem.

class Power2(exception_error=False, initial_value=1.0)[source]#

Power2 is a very basic quadratic analytical OptimizationProblem.

Objective to minimize: \(x_0^2 + x_1^2 + x_2^2\)
Inequality constraint 1: \(x_0^3 - 0.5 > 0\)
Inequality constraint 2: \(x_1^3 - 0.5 > 0\)
Equality constraint: \(x_2^3 - 0.9 = 0\)
Analytical optimum: \(x^*=(0.5^{1/3}, 0.5^{1/3}, 0.9^{1/3})\)

Parameters:

exception_error (bool) --
Whether to raise an error when calling the objective; useful for tests.

By default it is set to False.
initial_value (float) --
The initial design value of the problem.

By default it is set to 1.0.

static eq_constraint(x_dv)[source]#

Compute the equality constraint \(x_2^3 - 0.9 = 0\).

static eq_constraint_jac(x_dv)[source]#

Compute the gradient of the equality constraint.

static get_solution()[source]#

Return the analytical solution of the problem.

static ineq_constraint1(x_dv)[source]#

Compute the first inequality constraint \(x_0^3 - 0.5 > 0\).

static ineq_constraint1_jac(x_dv)[source]#

Compute the gradient of the first inequality constraint.

static ineq_constraint2(x_dv)[source]#

Compute the second inequality constraint \(x_1^3 - 0.5 > 0\).

static ineq_constraint2_jac(x_dv)[source]#

Compute the gradient of the second inequality constraint.

pow2(x_dv)[source]#

Compute the objective \(x_0^2 + x_1^2 + x_2^2\).

Parameters:: x_dv (ndarray) -- The design variable vector.
Returns:: The objective value.
Raises:: ValueError -- When exception_error is True and the method has already been called three times.
Return type:: ndarray

static pow2_jac(x_dv)[source]#

Compute the gradient of the objective.