def test_analytic_param_in_exponent(self) -> None:
# construct a problem with solution
# x^\star(\alpha) = 1 - 2^alpha, and derivative
# x^\star'(\alpha) = -log(2) * 2^\alpha
base = 2.0
alpha = cp.Parameter()
x = cp.Variable(pos=True)
objective = cp.Maximize(x)
constr = [cp.one_minus_pos(x) >= cp.Constant(base)**alpha]
problem = cp.Problem(objective, constr)
alpha.value = -1.0
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-6)
self.assertAlmostEqual(x.value, 1 - base**(-1.0))
problem.backward()
problem.derivative()
self.assertAlmostEqual(alpha.gradient, -np.log(base) * base**(-1.0))
self.assertAlmostEqual(x.delta, alpha.gradient * 1e-5, places=3)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
alpha.value = -1.2
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-6)
self.assertAlmostEqual(x.value, 1 - base**(-1.2))
problem.backward()
problem.derivative()
self.assertAlmostEqual(alpha.gradient, -np.log(base) * base**(-1.2))
self.assertAlmostEqual(x.delta, alpha.gradient * 1e-5, places=3)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
def test_one_minus_analytic(self) -> None:
# construct a problem with solution
# x^\star(\alpha) = 1 - \alpha^2, and derivative
# x^\star'(\alpha) = -2\alpha
alpha = cp.Parameter(pos=True)
x = cp.Variable(pos=True)
objective = cp.Maximize(x)
constr = [cp.one_minus_pos(x) >= alpha**2]
problem = cp.Problem(objective, constr)
alpha.value = 0.4
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-5)
self.assertAlmostEqual(x.value, 1 - 0.4**2, places=3)
problem.backward()
problem.derivative()
self.assertAlmostEqual(alpha.gradient, -2 * 0.4, places=3)
self.assertAlmostEqual(x.delta, -2 * 0.4 * 1e-5, places=3)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
alpha.value = 0.5
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-5)
problem.backward()
problem.derivative()
self.assertAlmostEqual(x.value, 1 - 0.5**2, places=3)
self.assertAlmostEqual(alpha.gradient, -2 * 0.5, places=3)
self.assertAlmostEqual(x.delta, -2 * 0.5 * 1e-5, places=3)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
def test_paper_example_one_minus_pos(self):
x = cvxpy.Variable(pos=True)
y = cvxpy.Variable(pos=True)
obj = cvxpy.Minimize(x * y)
constr = [(y * cvxpy.one_minus_pos(x / y))**2 >= 1, x >= y / 3]
problem = cvxpy.Problem(obj, constr)
# smoke test.
problem.solve(SOLVER, gp=True)
def test_one_minus_pos(self):
x = cvxpy.Variable(pos=True)
obj = cvxpy.Maximize(x)
constr = [cvxpy.one_minus_pos(x) >= 0.4]
problem = cvxpy.Problem(obj, constr)
problem.solve(SOLVER, gp=True)
self.assertAlmostEqual(problem.value, 0.6)
self.assertAlmostEqual(x.value, 0.6)
def test_one_minus_pos(self) -> None:
x = cp.Variable(pos=True)
a = cp.Parameter(pos=True, value=3)
b = cp.Parameter(pos=True, value=0.1)
obj = cp.Maximize(x)
constr = [cp.one_minus_pos(a * x) >= a * b]
problem = cp.Problem(obj, constr)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
def test_paper_example_one_minus_pos(self) -> None:
x = cp.Variable(pos=True)
y = cp.Variable(pos=True)
a = cp.Parameter(pos=True, value=2)
b = cp.Parameter(pos=True, value=1)
c = cp.Parameter(pos=True, value=3)
obj = cp.Minimize(x * y)
constr = [(y * cp.one_minus_pos(x / y))**a >= b, x >= y / c]
problem = cp.Problem(obj, constr)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, solve_methods=[s.SCS], gp=True, atol=1e-3)
def test_one_minus_pos(self):
x = cp.Variable(pos=True)
obj = cp.Maximize(x)
alpha = cp.Parameter(pos=True, value=0.1)
constr = [cp.one_minus_pos(alpha + x) >= 0.4]
problem = cp.Problem(obj, constr)
problem.solve(SOLVER, gp=True, enforce_dpp=True)
self.assertAlmostEqual(problem.value, 0.5)
self.assertAlmostEqual(x.value, 0.5)
alpha.value = 0.4
problem.solve(SOLVER, gp=True, enforce_dpp=True)
self.assertAlmostEqual(problem.value, 0.2)
self.assertAlmostEqual(x.value, 0.2)
def test_param_used_in_exponent_and_elsewhere(self) -> None:
# construct a problem with solution
# x^\star(\alpha) = 1 - 0.3^alpha - alpha^2, and derivative
# x^\star'(\alpha) = -log(0.3) * 0.2^\alpha - 2*alpha
base = 0.3
alpha = cp.Parameter(pos=True, value=0.5)
x = cp.Variable(pos=True)
objective = cp.Maximize(x)
constr = [cp.one_minus_pos(x) >= cp.Constant(base)**alpha + alpha**2]
problem = cp.Problem(objective, constr)
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-5)
self.assertAlmostEqual(x.value, 1 - base**(0.5) - 0.5**2)
problem.backward()
problem.derivative()
self.assertAlmostEqual(alpha.gradient,
-np.log(base) * base**(0.5) - 2 * 0.5)
self.assertAlmostEqual(x.delta, alpha.gradient * 1e-5, places=3)
def test_param_used_twice(self) -> None:
# construct a problem with solution
# x^\star(\alpha) = 1 - \alpha^2 - alpha^3, and derivative
# x^\star'(\alpha) = -2\alpha - 3\alpha^2
alpha = cp.Parameter(pos=True)
x = cp.Variable(pos=True)
objective = cp.Maximize(x)
constr = [cp.one_minus_pos(x) >= alpha**2 + alpha**3]
problem = cp.Problem(objective, constr)
alpha.value = 0.4
alpha.delta = 1e-5
problem.solve(solver=cp.DIFFCP, gp=True, requires_grad=True, eps=1e-6)
self.assertAlmostEqual(x.value, 1 - 0.4**2 - 0.4**3)
problem.backward()
problem.derivative()
self.assertAlmostEqual(alpha.gradient, -2 * 0.4 - 3 * 0.4**2)
self.assertAlmostEqual(x.delta, alpha.gradient * 1e-5)
gradcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
perturbcheck(problem, gp=True, solve_methods=[s.SCS], atol=1e-3)
