def solve_conic():
m = pmo.block()
m.x = pmo.variable(lb=0)
m.y = pmo.variable(lb=0)
m.z = pmo.variable(lb=0)
m.p = pmo.variable()
m.q = pmo.variable()
m.r = pmo.variable(lb=0)
m.k = pmo.block_tuple([
pmo.conic.primal_power.as_domain(r1=m.x, r2=m.y, x=[None], alpha=0.2),
pmo.conic.primal_power.as_domain(r1=m.z, r2=1, x=[None], alpha=0.4)
])
m.c = pmo.constraint(body=m.x + m.y + 0.5 * m.z, rhs=2)
m.o = pmo.objective(m.k[0].x[0] + m.k[1].x[0] - m.x, sense=pmo.maximize)
mosek = pmo.SolverFactory("mosek")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
print("conic solution:")
print("x: {0:.4f}, y: {1:.4f}, z: {2:.4f}".\
format(m.x(), m.y(), m.z()))
print("objective: {0: .5f}".\
format(m.o()))
print("")
def solve_conic():
m = pmo.block()
m.t = pmo.variable()
m.u = pmo.variable()
m.v = pmo.variable()
m.w = pmo.variable()
m.k = pmo.block_tuple([
# exp(u-t) + exp(2v + w - t) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.u - m.t),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=2*m.v + m.w - m.t),
# exp(0.5u + log(0.1)) + exp(-v + log(2)) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=0.5*m.u + pmo.log(0.1)),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=-m.v + pmo.log(2)),
# exp(-w) + exp(v-2u) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=-m.w),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.v - 2*m.u)])
m.c = pmo.constraint_tuple([
pmo.constraint(body=m.k[0].r + m.k[1].r,
ub=1),
pmo.constraint(body=m.k[2].r + m.k[3].r,
ub=1),
pmo.constraint(body=m.k[4].r + m.k[5].r,
ub=1)])
m.o = pmo.objective(m.t,
sense=pmo.minimize)
mosek = pmo.SolverFactory("mosek")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
x, y, z = pmo.exp(m.u()), pmo.exp(m.v()), pmo.exp(m.w())
print("conic solution:")
print("x: {0:.4f}, y: {1:.4f}, z: {2:.4f}".\
format(x, y, z))
print("objective: {0: .5f}".\
format(x + (y**2)*z))
print("")
def solve_conic():
m = pmo.block()
m.t = pmo.variable()
m.u = pmo.variable()
m.v = pmo.variable()
m.w = pmo.variable()
m.k = pmo.block_tuple([
# exp(u-t) + exp(2v + w - t) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.u - m.t),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=2*m.v + m.w - m.t),
# exp(0.5u + log(0.1)) + exp(-v + log(2)) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=0.5*m.u + pmo.log(0.1)),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=-m.v + pmo.log(2)),
# exp(-w) + exp(v-2u) <= 1
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=-m.w),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.v - 2*m.u)])
m.c = pmo.constraint_tuple([
pmo.constraint(body=m.k[0].r + m.k[1].r, ub=1),
pmo.constraint(body=m.k[2].r + m.k[3].r, ub=1),
pmo.constraint(body=m.k[4].r + m.k[5].r, ub=1)
])
m.o = pmo.objective(m.t, sense=pmo.minimize)
mosek = pmo.SolverFactory("mosek")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
x, y, z = pmo.exp(m.u()), pmo.exp(m.v()), pmo.exp(m.w())
print("conic solution:")
print("x: {0:.4f}, y: {1:.4f}, z: {2:.4f}".\
format(x, y, z))
print("objective: {0: .5f}".\
format(x + (y**2)*z))
print("")
def solve_conic(Aw, Af, alpha, beta, gamma, delta):
m = pmo.block()
m.x = pmo.variable()
m.y = pmo.variable()
m.z = pmo.variable()
m.k = pmo.block_tuple([
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.x + m.y + pmo.log(2.0/Aw)),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.x + m.z + pmo.log(2.0/Aw))])
m.c = pmo.constraint_tuple([
pmo.constraint(body=m.k[0].r + m.k[1].r,
ub=1),
pmo.constraint(body=m.y + m.z, ub=pmo.log(Af)),
pmo.constraint(lb=pmo.log(alpha),
body=m.x - m.y,
ub=pmo.log(beta)),
pmo.constraint(lb=pmo.log(gamma),
body=m.z - m.y,
ub=pmo.log(delta))])
m.o = pmo.objective(m.x + m.y + m.z,
sense=pmo.maximize)
mosek = pmo.SolverFactory("mosek")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
h, w, d = pmo.exp(m.x()), pmo.exp(m.y()), pmo.exp(m.z())
print("conic solution:")
print("h: {0:.4f}, w: {1:.4f}, d: {2:.4f}".\
format(h, w, d))
print("volume: {0: .5f}".\
format(h*w*d))
print("")
def solve_conic(Aw, Af, alpha, beta, gamma, delta):
m = pmo.block()
m.x = pmo.variable()
m.y = pmo.variable()
m.z = pmo.variable()
m.k = pmo.block_tuple([
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.x + m.y + pmo.log(2.0/Aw)),
pmo.conic.primal_exponential.\
as_domain(r=None,
x1=1,
x2=m.x + m.z + pmo.log(2.0/Aw))])
m.c = pmo.constraint_tuple([
pmo.constraint(body=m.k[0].r + m.k[1].r, ub=1),
pmo.constraint(body=m.y + m.z, ub=pmo.log(Af)),
pmo.constraint(lb=pmo.log(alpha), body=m.x - m.y, ub=pmo.log(beta)),
pmo.constraint(lb=pmo.log(gamma), body=m.z - m.y, ub=pmo.log(delta))
])
m.o = pmo.objective(m.x + m.y + m.z, sense=pmo.maximize)
mosek = pmo.SolverFactory("mosek_direct")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
h, w, d = pmo.exp(m.x()), pmo.exp(m.y()), pmo.exp(m.z())
print("conic solution:")
print("h: {0:.4f}, w: {1:.4f}, d: {2:.4f}".\
format(h, w, d))
print("volume: {0: .5f}".\
format(h*w*d))
print("")
def solve_conic():
m = pmo.block()
m.x = pmo.variable(lb=0)
m.y = pmo.variable(lb=0)
m.z = pmo.variable(lb=0)
m.p = pmo.variable()
m.q = pmo.variable()
m.r = pmo.variable(lb=0)
m.k = pmo.block_tuple([
pmo.conic.primal_power.as_domain(r1=m.x,
r2=m.y,
x=[None],
alpha=0.2),
pmo.conic.primal_power.as_domain(r1=m.z,
r2=1,
x=[None],
alpha=0.4)])
m.c = pmo.constraint(body=m.x + m.y + 0.5*m.z,
rhs=2)
m.o = pmo.objective(m.k[0].x[0] + m.k[1].x[0] - m.x,
sense=pmo.maximize)
mosek = pmo.SolverFactory("mosek")
result = mosek.solve(m)
assert str(result.solver.termination_condition) == "optimal"
print("conic solution:")
print("x: {0:.4f}, y: {1:.4f}, z: {2:.4f}".\
format(m.x(), m.y(), m.z()))
print("objective: {0: .5f}".\
format(m.o()))
print("")