def test_cp_method_on_third_analytical_example():
print('# Test Cutting Plane Method on Constrained Dual Analytical Example')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = ConstrainedDualAnalyticalExampleInnerProblem()
dual_method = CuttingPlanesMethod(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
epsilon=0.01,
sense='max')
dual_method.set_dual_domain(type='sum to param', param=0.5)
dual_method.lambda_k = dual_method.projection_function(np.array([-2,2]))
logger = EnhancedDualMethodLogger(dual_method)
for iteration in range(5):
# print(dual_method.lambda_k)
# print(dual_method.d_k)
dual_method.dual_step()
# Method should end close to lambda*, where lambda*[1] = 0.5 - lambda*[0], and 0<= lambda*[0] <= 0.5
lambda_star = logger.lambda_k_iterates[-1]
assert 0 <= lambda_star[0] <= 0.5
assert lambda_star[1] == 0.5 - lambda_star[0]
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1], -1.0, atol=0.01)
def test_UPGM_on_third_analytical_example_non_zero_start():
print(
'# Test UPGM on Third Analytical Example (constrained dual). Start at NON-0.'
)
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = ConstrainedDualAnalyticalExampleInnerProblem()
dual_method = UniversalPGM(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension)
# we set the initial point somewhere not 0
dual_method.lambda_hat_k = dual_method.projection_function(
np.array([-2, 2]))
logger = GenericDualMethodLogger(dual_method)
for iteration in range(5):
# print(dual_method.lambda_k)
# print(dual_method.lambda_tilde_k)
# print(dual_method.d_k)
dual_method.dual_step()
# Method should end close to lambda*, where lambda*[1] = 0.5 - lambda*[0], and 0<= lambda*[0] <= 0.5
lambda_star = logger.lambda_k_iterates[-1]
# print(lambda_star)
assert 0 <= lambda_star[0] <= 0.5
assert lambda_star[1] == 0.5 - lambda_star[0]
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1], -1.0, atol=0.01)