def getsocpconstrmultipliers(cplex, dslack=None):
socppi = dict()
# Compute full dual slack (sum of dual multipliers for bound constraints
# and per-constraint dual slacks)
dense = dict(
zip(cplex.variables.get_names(), cplex.solution.get_reduced_costs()))
for n in cplex.quadratic_constraints.get_names():
v = cplex.solution.get_quadratic_dualslack(n)
for (var, val) in zip(v.ind, v.val):
dense[cplex.variables.get_names(var)] += val
# Find the cone head variables and pick up the dual slacks for them.
for n in cplex.quadratic_constraints.get_names():
q = cplex.quadratic_constraints.get_quadratic_components(n)
for (i1, i2, v) in zip(q.ind1, q.ind2, q.val):
if v < 0:
name = cplex.variables.get_names(i1)
socppi[n] = dense[name]
break
if dslack is not None:
dslack.clear()
for key, value in six.iteritems(dense):
dslack[key] = value
return socppi
def getsocpconstrmultipliers(cplex,dslack = None):
socppi = dict()
# Compute full dual slack (sum of dual multipliers for bound constraints
# and per-constraint dual slacks)
dense = dict(zip(cplex.variables.get_names(),
cplex.solution.get_reduced_costs()))
for n in cplex.quadratic_constraints.get_names():
v = cplex.solution.get_quadratic_dualslack(n)
for (var,val) in zip(v.ind, v.val):
dense[cplex.variables.get_names(var)] += val
# Find the cone head variables and pick up the dual slacks for them.
for n in cplex.quadratic_constraints.get_names():
q = cplex.quadratic_constraints.get_quadratic_components(n)
for (i1,i2,v) in zip(q.ind1, q.ind2, q.val):
if v < 0:
name = cplex.variables.get_names(i1)
socppi[n] = dense[name]
break
if dslack != None:
dslack.clear()
for key, value in six.iteritems(dense):
dslack[key] = value
return socppi
def checkkkt(c, cone, tol):
# Read primal and dual solution information.
x = dict(zip(c.variables.get_names(), c.solution.get_values()))
s = dict(
zip(c.linear_constraints.get_names(), c.solution.get_linear_slacks()))
pi = dict(
zip(c.linear_constraints.get_names(), c.solution.get_dual_values()))
dslack = dict()
for key, value in six.iteritems(getsocpconstrmultipliers(c, dslack)):
pi[key] = value
for (q, v) in zip(
c.quadratic_constraints.get_names(),
c.solution.get_quadratic_slacks(
c.quadratic_constraints.get_names())):
s[q] = v
# Print out the data just fetched.
print("x = [", end=' ')
for n in c.variables.get_names():
print(" %7.3f" % x[n], end=' ')
print(" ]")
print("dslack = [", end=' ')
for n in c.variables.get_names():
print(" %7.3f" % dslack[n], end=' ')
print(" ]")
print("pi = [", end=' ')
for n in c.linear_constraints.get_names():
print(" %7.3f" % pi[n], end=' ')
for n in c.quadratic_constraints.get_names():
print(" %7.3f" % pi[n], end=' ')
print(" ]")
print("slack = [", end=' ')
for n in c.linear_constraints.get_names():
print(" %7.3f" % s[n], end=' ')
for n in c.quadratic_constraints.get_names():
print(" %7.3f" % s[n], end=' ')
print(" ]")
# Test primal feasibility.
# This example illustrates the use of dual vectors returned by CPLEX
# to verify dual feasibility, so we do not test primal feasibility
# here.
# Test dual feasibility.
# We must have
# - for all <= constraints the respective pi value is non-negative,
# - for all >= constraints the respective pi value is non-positive,
# - the dslack value for all non-cone variables must be non-negative.
# Note that we do not support ranged constraints here.
for n in c.linear_constraints.get_names():
if c.linear_constraints.get_senses(n) == 'L' and pi[n] < -tol:
print("Dual multiplier ",
pi[n],
" for <= constraint ",
n,
" not feasible.",
file=sys.stderr)
return False
elif c.linear_constraints.get_senses(n) == 'G' and pi[n] > tol:
print("Dual multiplier ",
pi[n],
" for >= constraint ",
n,
" not feasible.",
file=sys.stderr)
return False
for n in c.quadratic_constraints.get_names():
if c.quadratic_constraints.get_senses(n) == 'L' and pi[n] < -tol:
print("Dual multiplier ",
pi[n],
" for <= constraint ",
n,
" not feasible.",
file=sys.stderr)
return False
elif c.quadratic_constraints.get_senses(n) == 'G' and pi[n] > tol:
print("Dual multiplier ",
pi[n],
" for >= constraint ",
n,
" not feasible.",
file=sys.stderr)
return False
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE and dslack[n] < -tol:
print("Dual multiplier for ",
n,
" is not feasible: ",
dslack[n],
file=sys.stderr)
return False
# Test complementary slackness.
# For each constraint either the constraint must have zero slack or
# the dual multiplier for the constraint must be 0. We must also
# consider the special case in which a variable is not explicitly
# contained in a second order cone constraint.
for n in c.linear_constraints.get_names():
if fabs(s[n]) > tol and fabs(pi[n]) > tol:
print("Invalid complementary slackness for ",
n,
": ",
s[n],
" and ",
pi[n],
file=sys.stderr)
return False
for n in c.quadratic_constraints.get_names():
if fabs(s[n]) > tol and fabs(pi[n]) > tol:
print("Invalid complementary slackness for ",
n,
": ",
s[n],
" and ",
pi[n],
file=sys.stderr)
return False
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE:
if fabs(x[n]) > tol and fabs(dslack[n]) > tol:
print("Invalid complementary slackness for ",
n,
": ",
x[n],
" and ",
dslack[n],
file=sys.stderr)
return False
# Test stationarity.
# We must have
# c - g[i]'(X)*pi[i] = 0
# where c is the objective function, g[i] is the i-th constraint of the
# problem, g[i]'(x) is the derivate of g[i] with respect to x and X is the
# optimal solution.
# We need to distinguish the following cases:
# - linear constraints g(x) = ax - b. The derivative of such a
# constraint is g'(x) = a.
# - second order constraints g(x[1],...,x[n]) = -x[1] + |(x[2],...,x[n])|
# the derivative of such a constraint is
# g'(x) = (-1, x[2]/|(x[2],...,x[n])|, ..., x[n]/|(x[2],...,x[n])|
# (here |.| denotes the Euclidean norm).
# - bound constraints g(x) = -x for variables that are not explicitly
# contained in any second order cone constraint. The derivative for
# such a constraint is g'(x) = -1.
# Note that it may happen that the derivative of a second order cone
# constraint is not defined at the optimal solution X (this happens if
# X=0). In this case we just skip the stationarity test.
val = dict(zip(c.variables.get_names(), c.objective.get_linear()))
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE:
val[n] -= dslack[n]
for n in c.linear_constraints.get_names():
r = c.linear_constraints.get_rows(n)
for j in range(0, len(r.ind)):
nj = c.variables.get_names(r.ind[j])
val[nj] -= r.val[j] * pi[n]
for n in c.quadratic_constraints.get_names():
r = c.quadratic_constraints.get_quadratic_components(n)
norm = 0
for j in range(0, len(r.ind1)):
nj = c.variables.get_names(r.ind1[j])
if r.val[j] > 0:
norm += x[nj] * x[nj]
norm = sqrt(norm)
if fabs(norm) <= tol:
# Derivative is not defined. Skip test.
print("Cannot test stationarity at non-differentiable point.",
file=sys.stderr)
return True
for j in range(0, len(r.ind1)):
nj = c.variables.get_names(r.ind1[j])
if r.val[j] < 0:
val[nj] -= pi[n]
else:
val[nj] += pi[n] * x[nj] / norm
# Now test that all elements in val[] are 0.
for n in c.variables.get_names():
if fabs(val[n]) > tol:
print("Invalid stationarity ", val[n], " for ", n, file=sys.stderr)
return False
return True
def checkkkt(c, cone, tol):
# Read primal and dual solution information.
x = dict(zip(c.variables.get_names(), c.solution.get_values()))
s = dict(zip(c.linear_constraints.get_names(), c.solution.get_linear_slacks()))
pi = dict(zip(c.linear_constraints.get_names(), c.solution.get_dual_values()))
dslack = dict()
for key,value in six.iteritems(getsocpconstrmultipliers(c, dslack)):
pi[key] = value
for (q,v) in zip(c.quadratic_constraints.get_names(),
c.solution.get_quadratic_slacks(c.quadratic_constraints.get_names())):
s[q] = v
# Print out the data just fetched.
print("x = [", end=' ')
for n in c.variables.get_names():
print(" %7.3f" % x[n], end=' ')
print(" ]")
print("dslack = [", end=' ')
for n in c.variables.get_names():
print(" %7.3f" % dslack[n], end=' ')
print(" ]")
print("pi = [", end=' ')
for n in c.linear_constraints.get_names():
print(" %7.3f" % pi[n], end=' ')
for n in c.quadratic_constraints.get_names():
print(" %7.3f" % pi[n], end=' ')
print(" ]")
print("slack = [", end=' ')
for n in c.linear_constraints.get_names():
print(" %7.3f" % s[n], end=' ')
for n in c.quadratic_constraints.get_names():
print(" %7.3f" % s[n], end=' ')
print(" ]")
# Test primal feasibility.
# This example illustrates the use of dual vectors returned by CPLEX
# to verify dual feasibility, so we do not test primal feasibility
# here.
# Test dual feasibility.
# We must have
# - for all <= constraints the respective pi value is non-negative,
# - for all >= constraints the respective pi value is non-positive,
# - the dslack value for all non-cone variables must be non-negative.
# Note that we do not support ranged constraints here.
for n in c.linear_constraints.get_names():
if c.linear_constraints.get_senses(n) == 'L' and pi[n] < -tol:
print("Dual multiplier ", pi[n], " for <= constraint ", n, " not feasible.", file=sys.stderr)
return False
elif c.linear_constraints.get_senses(n) == 'G' and pi[n] > tol:
print("Dual multiplier ", pi[n], " for >= constraint ", n, " not feasible.", file=sys.stderr)
return False
for n in c.quadratic_constraints.get_names():
if c.quadratic_constraints.get_senses(n) == 'L' and pi[n] < -tol:
print("Dual multiplier ", pi[n], " for <= constraint ", n, " not feasible.", file=sys.stderr)
return False
elif c.quadratic_constraints.get_senses(n) == 'G' and pi[n] > tol:
print("Dual multiplier ", pi[n], " for >= constraint ", n, " not feasible.", file=sys.stderr)
return False
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE and dslack[n] < -tol:
print("Dual multiplier for ", n, " is not feasible: ", dslack[n], file=sys.stderr)
return False
# Test complementary slackness.
# For each constraint either the constraint must have zero slack or
# the dual multiplier for the constraint must be 0. We must also
# consider the special case in which a variable is not explicitly
# contained in a second order cone constraint.
for n in c.linear_constraints.get_names():
if fabs(s[n]) > tol and fabs(pi[n]) > tol:
print("Invalid complementary slackness for ", n, ": ", s[n], " and ", pi[n], file=sys.stderr)
return False
for n in c.quadratic_constraints.get_names():
if fabs(s[n]) > tol and fabs(pi[n]) > tol:
print("Invalid complementary slackness for ", n, ": ", s[n], " and ", pi[n], file=sys.stderr)
return False
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE:
if fabs(x[n]) > tol and fabs(dslack[n]) > tol:
print("Invalid complementary slackness for ", n, ": ", x[n], " and ", dslack[n], file=sys.stderr)
return False
# Test stationarity.
# We must have
# c - g[i]'(X)*pi[i] = 0
# where c is the objective function, g[i] is the i-th constraint of the
# problem, g[i]'(x) is the derivate of g[i] with respect to x and X is the
# optimal solution.
# We need to distinguish the following cases:
# - linear constraints g(x) = ax - b. The derivative of such a
# constraint is g'(x) = a.
# - second order constraints g(x[1],...,x[n]) = -x[1] + |(x[2],...,x[n])|
# the derivative of such a constraint is
# g'(x) = (-1, x[2]/|(x[2],...,x[n])|, ..., x[n]/|(x[2],...,x[n])|
# (here |.| denotes the Euclidean norm).
# - bound constraints g(x) = -x for variables that are not explicitly
# contained in any second order cone constraint. The derivative for
# such a constraint is g'(x) = -1.
# Note that it may happen that the derivative of a second order cone
# constraint is not defined at the optimal solution X (this happens if
# X=0). In this case we just skip the stationarity test.
val = dict(zip(c.variables.get_names(), c.objective.get_linear()))
for n in c.variables.get_names():
if cone[n] == NOT_IN_CONE:
val[n] -= dslack[n]
for n in c.linear_constraints.get_names():
r = c.linear_constraints.get_rows(n)
for j in range(0, len(r.ind)):
nj = c.variables.get_names(r.ind[j])
val[nj] -= r.val[j] * pi[n]
for n in c.quadratic_constraints.get_names():
r = c.quadratic_constraints.get_quadratic_components(n)
norm = 0
for j in range(0, len(r.ind1)):
nj = c.variables.get_names(r.ind1[j])
if r.val[j] > 0:
norm += x[nj] * x[nj]
norm = sqrt(norm)
if fabs(norm) <= tol:
# Derivative is not defined. Skip test.
print("Cannot test stationarity at non-differentiable point.", file=sys.stderr)
return True
for j in range(0, len(r.ind1)):
nj = c.variables.get_names(r.ind1[j])
if r.val[j] < 0:
val[nj] -= pi[n]
else:
val[nj] += pi[n] * x[nj] / norm
# Now test that all elements in val[] are 0.
for n in c.variables.get_names():
if fabs(val[n]) > tol:
print("Invalid stationarity ", val[n], " for ", n, file=sys.stderr)
return False
return True