def test_curvature(self) -> None:
x = cp.Variable(3)
expr = cp.length(x)
self.assertEqual(expr.curvature, s.QUASICONVEX)
expr = -cp.length(x)
self.assertEqual(expr.curvature, s.QUASICONCAVE)
expr = cp.ceil(x)
self.assertEqual(expr.curvature, s.QUASILINEAR)
self.assertTrue(expr.is_quasilinear())
def test_min(self) -> None:
x = cp.Variable(2)
expr = cp.min(cp.ceil(x))
problem = cp.Problem(cp.Maximize(expr),
[x[0] >= 11.9, x[0] <= 15.8, x[1] >= 17.4])
self.assertTrue(problem.is_dqcp())
problem.solve(SOLVER, qcp=True)
self.assertAlmostEqual(problem.objective.value, 16.0)
self.assertLess(x[0].value, 16.0)
self.assertGreater(x[0].value, 14.9)
self.assertGreater(x[1].value, 17.3)
def test_flip_bounds(self) -> None:
x = cp.Variable(pos=True)
problem = cp.Problem(cp.Maximize(cp.ceil(x)), [x <= 1])
problem.solve(SOLVER, qcp=True, low=0, high=0.5)
self.assertGreater(x.value, 0)
self.assertLessEqual(x.value, 1)
problem.solve(SOLVER, qcp=True, low=0, high=None)
self.assertGreater(x.value, 0)
self.assertLessEqual(x.value, 1)
problem.solve(SOLVER, qcp=True, low=None, high=0.5)
self.assertGreater(x.value, 0)
self.assertLessEqual(x.value, 1)
def test_tutorial_dqcp(self):
# The sign of variables affects curvature analysis.
x = cp.Variable(nonneg=True)
concave_frac = x * cp.sqrt(x)
constraint = [cp.ceil(x) <= 10]
problem = cp.Problem(cp.Maximize(concave_frac), constraint)
self.assertTrue(concave_frac.is_quasiconcave())
self.assertTrue(constraint[0].is_dqcp())
self.assertTrue(problem.is_dqcp())
w = cp.Variable()
fn = w * cp.sqrt(w)
problem = cp.Problem(cp.Maximize(fn))
self.assertFalse(fn.is_dqcp())
self.assertFalse(problem.is_dqcp())
def test_basic_maximization_with_interval(self):
x = cp.Variable()
expr = cp.ceil(x)
self.assertTrue(expr.is_dqcp())
self.assertTrue(expr.is_quasiconvex())
self.assertTrue(expr.is_quasiconcave())
self.assertFalse(expr.is_convex())
self.assertFalse(expr.is_concave())
self.assertFalse(expr.is_dcp())
self.assertFalse(expr.is_dgp())
problem = cp.Problem(cp.Maximize(expr), [x >= 12, x <= 17])
self.assertTrue(problem.is_dqcp())
self.assertFalse(problem.is_dcp())
self.assertFalse(problem.is_dgp())
problem.solve(SOLVER, qcp=True)
self.assertAlmostEqual(x.value, 17.0, places=3)
def test_basic_solve(self):
x = cp.Variable()
expr = cp.ceil(x)
self.assertTrue(expr.is_dqcp())
self.assertTrue(expr.is_quasiconvex())
self.assertTrue(expr.is_quasiconcave())
self.assertFalse(expr.is_convex())
self.assertFalse(expr.is_concave())
self.assertFalse(expr.is_dcp())
self.assertFalse(expr.is_dgp())
problem = cp.Problem(cp.Minimize(expr), [x >= 12, x <= 17])
self.assertTrue(problem.is_dqcp())
self.assertFalse(problem.is_dcp())
self.assertFalse(problem.is_dgp())
problem.solve(SOLVER, qcp=True, low=12, high=17)
self.assertAlmostEqual(problem.value, 12.0, places=3)
self.assertAlmostEqual(x.value, 12.0, places=3)
problem._clear_solution()
problem.solve(SOLVER, qcp=True)
self.assertAlmostEqual(problem.value, 12.0, places=3)
self.assertAlmostEqual(x.value, 12.0, places=3)
problem._clear_solution()
problem.solve(SOLVER, qcp=True, high=17)
self.assertAlmostEqual(problem.value, 12.0, places=3)
self.assertAlmostEqual(x.value, 12.0, places=3)
problem._clear_solution()
problem.solve(SOLVER, qcp=True, low=12)
self.assertAlmostEqual(problem.value, 12.0, places=3)
self.assertAlmostEqual(x.value, 12.0, places=3)
problem._clear_solution()
problem.solve(SOLVER, qcp=True, low=0, high=100)
self.assertAlmostEqual(problem.value, 12.0, places=3)
self.assertAlmostEqual(x.value, 12.0, places=3)
def test_basic_composition(self):
x, y = cp.Variable(2)
expr = cp.maximum(cp.ceil(cp.ceil(x)), cp.ceil(cp.ceil(y)))
problem = cp.Problem(cp.Minimize(expr), [x >= 12, x <= 17, y >= 17.4])
self.assertTrue(problem.is_dqcp())
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 18.0)
self.assertLess(x.value, 17.1)
self.assertGreater(x.value, 11.9)
self.assertGreater(y.value, 17.3)
# This problem should have the same solution.
expr = cp.maximum(cp.floor(cp.ceil(x)), cp.floor(cp.ceil(y)))
problem = cp.Problem(cp.Minimize(expr), [x >= 12, x <= 17, y >= 17.4])
self.assertTrue(problem.is_dqcp())
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 18.0)
self.assertLess(x.value, 17.1)
self.assertGreater(x.value, 11.9)
self.assertGreater(y.value, 17.3)
def test_noop_logistic_constr(self):
x = cp.Variable(nonneg=True)
constr = [cp.logistic(cp.ceil(x)) >= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.status, s.OPTIMAL)
def test_noop_inv_pos_constr(self):
x = cp.Variable()
constr = [cp.inv_pos(cp.ceil(x)) >= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.status, s.OPTIMAL)
def test_infeasible_logistic_constr(self):
x = cp.Variable(nonneg=True)
constr = [cp.logistic(cp.ceil(x)) <= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.status, s.INFEASIBLE)
def test_infeasible(self):
x = cp.Variable(2)
problem = cp.Problem(cp.Minimize(cp.length(x)),
[x == -1, cp.ceil(x) >= 1])
problem.solve(SOLVER, qcp=True)
self.assertIn(problem.status, (s.INFEASIBLE, s.INFEASIBLE_INACCURATE))
def solve_problem_func(env, alpha_parameter):
# ----------parameters----------
I = env["I"]
M = env["M"]
h_ul = env["h_ul"]
bandwidth_max = env["bandwidth_max"]
tx_power_m_max = env["tx_power_m_max"]
comp_bs = env["comp_bs"]
comp_m = env["comp_m"]
task = env["task"]
data = env["data"]
M_list = env["M_list"]
time_scale = env["time_scale"]
rate_m_itr = bandwidth_max * np.log2(1 + tx_power_m_max * h_ul)
average_rate = bandwidth_max * np.log2(1 + tx_power_m_max * h_ul) / M
alpha_v = alpha_parameter
# ----------itration variable parameter----------
# this part is defined to use the iteration variable in the subproblem
# ----------variables----------
# define the variables
# bandwidth allocation factor w
omega = cp.Variable([M, I])
# offloading factor alpha
alpha = cp.Variable([M, I])
# bs sever allocation factor beta
beta = cp.Variable([M, I])
eta = cp.Variable([M, I])
mu = cp.Variable([M, I])
# max delay T
T = cp.Variable()
# additional variables
t1 = cp.Variable()
t2 = cp.Variable()
t3 = cp.Variable()
# ----------problem formulation----------
# --------objective function--------
objective_func = T
objective1 = cp.Minimize(objective_func)
# --------constraints--------
# offloading constraints
c1 = [alpha >= 0, alpha <= 1]
# bandwidth allocation constraints
c4_5 = [cp.sum(omega) <= 1, omega >= (1e-7)]
# bs server allocation constraints
c2_3 = [cp.sum(beta) <= 1, beta >= (1e-7)]
c6 = [cp.multiply(1 - alpha, task) / comp_m * time_scale <= t1]
c7b = [
-cp.log(t3) - cp.log(beta) + np.log2(alpha_v) +
cp.multiply(1 / alpha_v / np.log(2),
(alpha - alpha_v)) + np.log2(task / comp_bs * time_scale)
<= 0
]
c8b = [
-cp.log(t2) - cp.log(omega) + np.log2(alpha_v) + cp.multiply(
1 / alpha_v / np.log(2),
(alpha - alpha_v)) + np.log2(data / rate_m_itr * time_scale) <= 0
]
#c8 = [cp.multiply(eta,task/comp_bs)*time_scale<=t3]
#c7 = [cp.multiply ( mu, data / rate_m_itr)*time_scale<=t2]
R1a2 = []
for i in range(0, M):
for j in range(0, I):
R1a2 = R1a2 + [
cp.norm(cp.vstack([2 * (alpha[i, j]), eta[i, j] - beta[i, j]]),
2) <= eta[i, j] + beta[i, j]
]
#assert R1a2[0].is_dqcp()
R1a3 = [alpha <= 1e7 * beta + (1e-7) * eta - 1, alpha <= eta]
R2a3 = [alpha <= 1e7 * omega + (1e-7) * mu - 1, alpha <= mu]
R2a4 = [eta <= 1e7, mu <= 1e7]
# local computing constraints R1
#R1 = [cp.ceil(cp.multiply(alpha, task)/comp_m) <= T]
R1 = [cp.ceil(cp.multiply(1 - alpha, task) / comp_m) - T <= 0]
#R1 = [cp.ceil(alpha) - 10 <= 0]
#assert R1[0].is_dqcp ()
# offloading constraints R2
R2a = cp.ceil(
cp.multiply(cp.multiply(alpha, task / comp_bs), cp.inv_pos(beta)))
R2b = cp.ceil(
cp.multiply(
cp.multiply(
alpha,
data / bandwidth_max * np.log2(1 + tx_power_m_max * h_ul)),
cp.inv_pos(omega)))
R2 = [R2a + R2b <= T]
R2a1 = cp.ceil((cp.multiply(eta, task / comp_bs)))
objective2 = cp.Minimize(
1 / 2 * cp.max(cp.ceil(cp.multiply(alpha, task) / comp_m)))
objective2 = cp.Minimize(
cp.max(cp.ceil(cp.multiply(1 - alpha, task / beta / comp_bs))))
obj3_part1 = 1 / 2 * cp.max(cp.ceil(cp.multiply(1 - alpha, task / comp_m)))
obj3_part1 = 1 / 2 * cp.ceil(cp.max(cp.multiply(1 - alpha, task / comp_m)))
obj3_part2 = 1 / 2 * cp.max(
cp.ceil(cp.multiply(eta, task / comp_bs)) +
cp.ceil(cp.multiply(mu, data / rate_m_itr)))
obj3_part2 = 1 / 2 * cp.ceil(cp.max(cp.multiply(
eta, task / comp_bs))) + 1 / 2 * cp.ceil(
cp.max(cp.multiply(mu, data / rate_m_itr)))
obj3_part3 = cp.abs(obj3_part1 - obj3_part2)
objective3 = cp.Minimize(obj3_part1 + obj3_part2 + obj3_part3)
#assert obj3_part1.is_dqcp ()
#assert obj3_part1.is_dcp()
#assert (cp.max(cp.ceil(cp.multiply(eta,task/comp_bs)))).is_dqcp()
#assert (cp.max(cp.ceil(cp.multiply(eta,task/comp_bs)))).is_dcp()
#assert (cp.ceil(cp.multiply(mu,data/rate_m_itr))).is_dqcp
#assert (cp.ceil(alpha)+cp.ceil(beta)).is_dqcp()
#assert obj3_part2.is_dqcp ()
#assert obj3_part3.is_dqcp ()
#assert objective3.is_dqcp ()
t = cp.Variable([M, I])
objective2 = cp.Minimize(cp.max(cp.ceil(cp.multiply(t, task / comp_bs))))
c4 = [(1 - alpha) / beta <= t]
objective6 = cp.Minimize(1 / 2 *
cp.ceil(t1 + t2 + t3 + cp.abs(t1 - t2 - t3)) +
3 / 2)
rho = 1
upsilon = 1
varsigma = 1e-27
obj7_func1 = 1 / 2 * cp.ceil(t1 + t2 + t3 + cp.abs(t1 - t2 - t3)) + 3 / 2
obj7_func1 = 1 / 2 * (t1 + t2 + t3 + cp.abs(t1 - t2 - t3))
obj7_func2 = cp.sum(
cp.multiply(1 - alpha, varsigma * task * np.square(comp_m))) + cp.sum(
tx_power_m_max * cp.multiply(mu, data / rate_m_itr))
objective7 = cp.Minimize(rho * obj7_func1 + upsilon * obj7_func2)
try:
# ----------probalem solve and results----------
# problem6 = cp.Problem(objective6, c1+c2_3+c4_5+c6+c7+c8+R1a3+R2a3+R2a4)
problem6 = cp.Problem(objective6, c1 + c2_3 + c4_5 + c6 + c7b + c8b)
problem6.solve(qcp=True, verbose=True, solver=cp.ECOS)
print()
print("problem1 solve: ", problem6.value)
print("alpha.value", alpha.value)
print("beta.value", beta.value)
print("omega.value", omega.value)
np.ceil(data / rate_m_itr * M * time_scale)
# ----------data collection and depict-----------
plt.clf()
plt.subplot(441)
plt.title("user_rate in M/s")
# plt.bar(x=M_list, height=(average_rate/1e6).reshape(M), width=1)
plt.plot(M_list,
omega.value * rate_m_itr / 1e6,
'-*',
color='b',
label="optimized rate")
plt.plot(M_list,
average_rate / 1e6,
'-o',
color='r',
label="average bandwidth allocation rate")
plt.legend()
plt.subplot(442)
plt.title("data transmitting delay")
plt.plot(
M_list,
data / average_rate * time_scale,
'-*',
color='b',
label=
"full date transmitting delay with average bandwidth allocation")
plt.plot(M_list, (alpha.value * data) / (omega.value * rate_m_itr) *
time_scale,
'-o',
color='r',
label="optimized transmitting delay")
# plt.bar(x=M_list, height=np.ceil(data / average_rate*time_scale).reshape(M), width=1)
plt.legend(fontsize='xx-small')
plt.subplot(443)
plt.title("local_computing_delay")
bar_width = 0.3
plt.bar(x=M_list,
height=np.ceil(time_scale * task / comp_m).reshape(M),
width=bar_width,
label='full local computing delay')
plt.bar(x=M_list + bar_width,
height=np.ceil(time_scale * (1 - alpha.value) * task /
comp_m).reshape(M),
width=bar_width,
label='remain local computing delay')
plt.plot(M_list,
problem6.value * np.ones(M),
'o',
color='m',
label="optimized delay")
plt.legend(fontsize='xx-small') # 显示图例，即label
plt.xticks(x=M_list +
bar_width / 2) # 显示x坐标轴的标签,即tick_label,调整位置，使其落在两个直方图中间位置
plt.subplot(444)
plt.title("offloading_computing_delay")
bar_width = 0.3 # 设置柱状图的宽度
plt.bar(x=M_list,
height=(np.ceil(task / (comp_bs / M)) * time_scale).reshape(M),
width=bar_width,
label='average full offloading computing delay')
plt.bar(x=M_list + bar_width,
height=(np.ceil(task * alpha.value / (beta.value * comp_bs) *
time_scale)).reshape(M),
width=bar_width,
label='optimized offloading computing delay')
# 绘制并列柱状图
plt.legend() # 显示图例，即label
plt.xticks(x=M_list +
bar_width / 2) # 显示x坐标轴的标签,即tick_label,调整位置，使其落在两个直方图中间位置
plt.subplot(445)
plt.title("optimized local computing_delay gain")
plt.plot(M_list, (problem6.value -
np.ceil(task / comp_m * time_scale)).reshape(M),
'x',
color='r')
plt.plot(M_list,
problem6.value * np.ones(M),
'o',
color='m',
label="optimized delay")
plt.plot(M_list,
t1.value * np.ones(M),
'v',
color='g',
label="local computing delay t1")
plt.plot(M_list,
t3.value * np.ones(M),
'^',
color='k',
label="offloading computing delay t3")
plt.plot(M_list,
t2.value * np.ones(M),
'*',
color='b',
label="transmitting delay t2")
plt.legend(fontsize='xx-small')
plt.subplot(446)
plt.title("optimized alpha beta")
plt.plot(M_list, alpha.value, '-v', label='alpha')
plt.plot(M_list, beta.value, '-x', label='beta')
plt.plot(M_list, omega.value, '^', label='omega')
plt.legend()
plt.subplot(447)
plt.title("optimized omega")
plt.plot(M_list, omega.value, '-^')
plt.subplot(448)
plt.title("optimized beta")
plt.plot(M_list, beta.value, '-^')
'''
plt.subplot(449)
plt.title("optimized eta")
plt.plot(M_list, eta.value,'-^')
plt.subplot(4,4,10)
plt.title("optimized mu")
plt.plot(M_list, mu.value,'-^')
plt.subplot(4,4,11)
plt.title("recalculated omega")
plt.plot(M_list, alpha.value/eta.value,'-^')
plt.subplot(4,4,12)
plt.title("recalculated beta")
plt.plot(M_list, alpha.value/mu.value,'-^')
'''
print("func1.value", obj7_func1.value)
print(
"local computing energy",
cp.sum(cp.multiply(1 - alpha,
varsigma * task * np.square(comp_m))).value)
print(
"offloading energy",
cp.sum(tx_power_m_max * cp.multiply(mu, data / rate_m_itr)).value)
print("func2.value", obj7_func2.value)
problem_result = {
"problem6.value": problem6.value,
"alpha.value": alpha.value
}
return problem_result
except SolverError:
problem6.value = 0
problem_result = {
"problem6.value": problem6.value,
"alpha.value": alpha_v
}
return problem_result
pass
def test_infeasible_exp_constr(self):
x = cp.Variable()
constr = [cp.exp(cp.ceil(x)) <= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(qcp=True)
self.assertEqual(problem.status, s.INFEASIBLE)
import cvxpy as cp import numpy as np import mosek, sys env = mosek.Env() env.set_Stream(mosek.streamtype.log, lambda x: sys.stdout.write(x)) env.echointro(1) x = cp.Variable () y = cp.Variable () t = cp.Variable(pos=True) objective_fn = cp.ceil ( x + y + cp.abs(x-y)) objective = cp.Minimize ( objective_fn+1 ) #constraint = cp.ceil ( x + y) <= t print((cp.ceil ( x + y + cp.abs(x-y))+1).curvature) problem = cp.Problem ( objective, [x<=2,y<=3,x>=0.5,y>=0.5] ) problem.solve ( qcp=True ) print ( "Optimal value: ", problem.value ) print ( "x: ", x.value ) print ( "y: ", y.value ) # Generate a random problem