def _create_using(self, model, **kwds):
"""
Tranform a model to its Lagrangian dual.
"""
# Optional naming schemes for dual variables and constraints
constraint_suffix = kwds.pop("dual_constraint_suffix", "_constraint")
variable_prefix = kwds.pop("dual_variable_prefix", "p_")
# Optional naming schemes to pass to StandardForm
sf_kwds = {}
sf_kwds["slack_names"] = kwds.pop("slack_names", "auxiliary_slack")
sf_kwds["excess_names"] = kwds.pop("excess_names", "auxiliary_excess")
sf_kwds["lb_names"] = kwds.pop("lb_names", "_lower_bound")
sf_kwds["ub_names"] = kwds.pop("ub_names", "_upper_bound")
sf_kwds["pos_suffix"] = kwds.pop("pos_suffix", "_plus")
sf_kwds["neg_suffix"] = kwds.pop("neg_suffix", "_minus")
# Get the standard form model
sf_transform = StandardForm()
sf = sf_transform(model, **sf_kwds)
# Roughly, parse the objectives and constraints to form A, b, and c of
#
# min c'x
# s.t. Ax = b
# x >= 0
#
# and create a new model from them.
# We use sparse matrix representations
# {constraint_name: {variable_name: coefficient}}
A = _sparse(lambda: _sparse(0))
# {constraint_name: coefficient}
b = _sparse(0)
# {variable_name: coefficient}
c = _sparse(0)
# Walk constaints
for (con_name, con_array) in sf.component_map(Constraint, active=True).items():
for con in (con_array[ndx] for ndx in con_array._index):
# The qualified constraint name
cname = "%s%s" % (variable_prefix, con.local_name)
# Process the body of the constraint
body_terms = process_canonical_repn(
generate_standard_repn(con.body))
# Add a numeric constant to the 'b' vector, if present
b[cname] -= body_terms.pop(None, 0)
# Add variable coefficients to the 'A' matrix
row = _sparse(0)
for (vname, coef) in body_terms.items():
row["%s%s" % (vname, constraint_suffix)] += coef
# Process the upper bound of the constraint. We rely on
# StandardForm to produce equality constraints, thus
# requiring us only to check the lower bounds.
lower_terms = process_canonical_repn(
generate_standard_repn(con.lower))
# Add a numeric constant to the 'b' matrix, if present
b[cname] += lower_terms.pop(None, 0)
# Add any variables to the 'A' matrix, if present
for (vname, coef) in lower_terms.items():
row["%s%s" % (vname, constraint_suffix)] -= coef
A[cname] = row
# Walk objectives. Multiply all coefficients by the objective's 'sense'
# to convert maximizing objectives to minimizing ones.
for (obj_name, obj_array) in sf.component_map(Objective, active=True).items():
for obj in (obj_array[ndx] for ndx in obj_array._index):
# The qualified objective name
# Process the objective
terms = process_canonical_repn(
generate_standard_repn(obj.expr))
# Add coefficients
for (name, coef) in terms.items():
c["%s%s" % (name, constraint_suffix)] += coef*obj_array.sense
# Form the dual
dual = AbstractModel()
# Make constraint index set
constraint_set_init = []
for (var_name, var_array) in sf.component_map(Var, active=True).items():
for var in (var_array[ndx] for ndx in var_array._index):
constraint_set_init.append("%s%s" %
(var.local_name, constraint_suffix))
# Make variable index set
variable_set_init = []
dual_variable_roots = []
for (con_name, con_array) in sf.component_map(Constraint, active=True).items():
for con in (con_array[ndx] for ndx in con_array._index):
dual_variable_roots.append(con.local_name)
variable_set_init.append("%s%s" % (variable_prefix, con.local_name))
# Create the dual Set and Var objects
dual.var_set = Set(initialize=variable_set_init)
dual.con_set = Set(initialize=constraint_set_init)
dual.vars = Var(dual.var_set)
# Make the dual constraints
def constraintRule(A, c, ndx, model):
return sum(A[v][ndx] * model.vars[v] for v in model.var_set) <= \
c[ndx]
dual.cons = Constraint(dual.con_set,
rule=partial(constraintRule, A, c))
# Make the dual objective (maximizing)
def objectiveRule(b, model):
return sum(b[v] * model.vars[v] for v in model.var_set)
dual.obj = Objective(rule=partial(objectiveRule, b), sense=maximize)
return dual.create()
def _create_using(self, model, **kwds):
"""
Tranform a model to its Lagrangian dual.
"""
# Optional naming schemes for dual variables and constraints
constraint_suffix = kwds.pop("dual_constraint_suffix", "_constraint")
variable_prefix = kwds.pop("dual_variable_prefix", "p_")
# Optional naming schemes to pass to StandardForm
sf_kwds = {}
sf_kwds["slack_names"] = kwds.pop("slack_names", "auxiliary_slack")
sf_kwds["excess_names"] = kwds.pop("excess_names", "auxiliary_excess")
sf_kwds["lb_names"] = kwds.pop("lb_names", "_lower_bound")
sf_kwds["ub_names"] = kwds.pop("ub_names", "_upper_bound")
sf_kwds["pos_suffix"] = kwds.pop("pos_suffix", "_plus")
sf_kwds["neg_suffix"] = kwds.pop("neg_suffix", "_minus")
# Get the standard form model
sf_transform = StandardForm()
sf = sf_transform(model, **sf_kwds)
# Roughly, parse the objectives and constraints to form A, b, and c of
#
# min c'x
# s.t. Ax = b
# x >= 0
#
# and create a new model from them.
# We use sparse matrix representations
# {constraint_name: {variable_name: coefficient}}
A = _sparse(lambda: _sparse(0))
# {constraint_name: coefficient}
b = _sparse(0)
# {variable_name: coefficient}
c = _sparse(0)
# Walk constaints
for (con_name, con_array) in sf.component_map(Constraint, active=True).items():
for con in (con_array[ndx] for ndx in con_array._index):
# The qualified constraint name
cname = "%s%s" % (variable_prefix, con.local_name)
# Process the body of the constraint
body_terms = process_canonical_repn(
generate_canonical_repn(con.body))
# Add a numeric constant to the 'b' vector, if present
b[cname] -= body_terms.pop(None, 0)
# Add variable coefficients to the 'A' matrix
row = _sparse(0)
for (vname, coef) in body_terms.items():
row["%s%s" % (vname, constraint_suffix)] += coef
# Process the upper bound of the constraint. We rely on
# StandardForm to produce equality constraints, thus
# requiring us only to check the lower bounds.
lower_terms = process_canonical_repn(
generate_canonical_repn(con.lower))
# Add a numeric constant to the 'b' matrix, if present
b[cname] += lower_terms.pop(None, 0)
# Add any variables to the 'A' matrix, if present
for (vname, coef) in lower_terms.items():
row["%s%s" % (vname, constraint_suffix)] -= coef
A[cname] = row
# Walk objectives. Multiply all coefficients by the objective's 'sense'
# to convert maximizing objectives to minimizing ones.
for (obj_name, obj_array) in sf.component_map(Objective, active=True).items():
for obj in (obj_array[ndx] for ndx in obj_array._index):
# The qualified objective name
# Process the objective
terms = process_canonical_repn(
generate_canonical_repn(obj.expr))
# Add coefficients
for (name, coef) in terms.items():
c["%s%s" % (name, constraint_suffix)] += coef*obj_array.sense
# Form the dual
dual = AbstractModel()
# Make constraint index set
constraint_set_init = []
for (var_name, var_array) in sf.component_map(Var, active=True).items():
for var in (var_array[ndx] for ndx in var_array._index):
constraint_set_init.append("%s%s" %
(var.local_name, constraint_suffix))
# Make variable index set
variable_set_init = []
dual_variable_roots = []
for (con_name, con_array) in sf.component_map(Constraint, active=True).items():
for con in (con_array[ndx] for ndx in con_array._index):
dual_variable_roots.append(con.local_name)
variable_set_init.append("%s%s" % (variable_prefix, con.local_name))
# Create the dual Set and Var objects
dual.var_set = Set(initialize=variable_set_init)
dual.con_set = Set(initialize=constraint_set_init)
dual.vars = Var(dual.var_set)
# Make the dual constraints
def constraintRule(A, c, ndx, model):
return sum(A[v][ndx] * model.vars[v] for v in model.var_set) <= \
c[ndx]
dual.cons = Constraint(dual.con_set,
rule=partial(constraintRule, A, c))
# Make the dual objective (maximizing)
def objectiveRule(b, model):
return sum(b[v] * model.vars[v] for v in model.var_set)
dual.obj = Objective(rule=partial(objectiveRule, b), sense=maximize)
return dual.create()