def _canonicalize_constraint(self, constr):
"""Recursively canonicalize a constraint."""
lhs = constr.args[0]
rhs = constr.args[1]
if isinstance(constr, Inequality):
lhs_val = np.array(lhs.value)
rhs_val = np.array(rhs.value)
if np.all(lhs_val == -np.inf) or np.all(rhs_val == np.inf):
# constraint is redundant
return [None]
elif np.any(lhs_val == np.inf) or np.any(rhs_val == -np.inf):
return [s.INFEASIBLE]
if constr.is_dcp():
canon_constr, aux_constr = self.canonicalize_tree(constr)
return [canon_constr] + aux_constr
# canonicalize lhs <= rhs
# either lhs or rhs is quasiconvex (and not convex)
assert isinstance(constr, Inequality)
# short-circuit zero-valued expressions to simplify inverse logic
if lhs.is_zero():
return self._canonicalize_constraint(0 <= rhs)
if rhs.is_zero():
return self._canonicalize_constraint(lhs <= 0)
if lhs.is_quasiconvex() and not lhs.is_convex():
# quasiconvex <= constant
assert rhs.is_constant(), rhs
if inverse.invertible(lhs):
# Apply inverse to both sides of constraint.
rhs = inverse.inverse(lhs)(rhs)
idx = lhs._non_const_idx()[0]
expr = lhs.args[idx]
if lhs.is_incr(idx):
return self._canonicalize_constraint(expr <= rhs)
return self._canonicalize_constraint(expr >= rhs)
elif isinstance(lhs, (maximum, max_atom)):
# Lower maximum.
return [
c for arg in lhs.args
for c in self._canonicalize_constraint(arg <= rhs)
]
else:
# Replace quasiconvex atom with a sublevel set.
canon_args, aux_args_constr = self._canon_args(lhs)
sublevel_set = sets.sublevel(lhs.copy(canon_args), t=rhs)
return sublevel_set + aux_args_constr
# constant <= quasiconcave
assert rhs.is_quasiconcave()
assert lhs.is_constant()
if inverse.invertible(rhs):
# Apply inverse to both sides of constraint.
lhs = inverse.inverse(rhs)(lhs)
idx = rhs._non_const_idx()[0]
expr = rhs.args[idx]
if rhs.is_incr(idx):
return self._canonicalize_constraint(lhs <= expr)
return self._canonicalize_constraint(lhs >= expr)
elif isinstance(rhs, (minimum, min_atom)):
# Lower minimum.
return [
c for arg in rhs.args
for c in self._canonicalize_constraint(lhs <= arg)
]
else:
# Replace quasiconcave atom with a superlevel set.
canon_args, aux_args_constr = self._canon_args(rhs)
superlevel_set = sets.superlevel(rhs.copy(canon_args), t=lhs)
return superlevel_set + aux_args_constr
def _canonicalize_constraint(self, constr):
"""Recursively canonicalize a constraint.
The DQCP grammar has expresions of the form
INCR* QCVX DCP
and
DECR* QCCV DCP
ie, zero or more real/scalar increasing (or decreasing) atoms, composed
with a quasiconvex (or quasiconcave) atom, composed with DCP
expressions.
The monotone functions are inverted by applying their inverses to
both sides of a constraint. The QCVX (QCCV) atom is lowered by
replacing it with its sublevel (superlevel) set. The DCP
expressions are canonicalized via graph implementations.
"""
lhs = constr.args[0]
rhs = constr.args[1]
if isinstance(constr, Inequality):
# taking inverses can yield +/- infinity; this is handled here.
lhs_val = np.array(lhs.value)
rhs_val = np.array(rhs.value)
if np.all(lhs_val == -np.inf) or np.all(rhs_val == np.inf):
# constraint is redundant
return [True]
elif np.any(lhs_val == np.inf) or np.any(rhs_val == -np.inf):
# constraint is infeasible
return [False]
if constr.is_dcp():
canon_constr, aux_constr = self.canonicalize_tree(constr)
return [canon_constr] + aux_constr
# canonicalize lhs <= rhs
# either lhs or rhs is quasiconvex (and not convex)
assert isinstance(constr, Inequality)
# short-circuit zero-valued expressions to simplify inverse logic
if lhs.is_zero():
return self._canonicalize_constraint(0 <= rhs)
if rhs.is_zero():
return self._canonicalize_constraint(lhs <= 0)
if lhs.is_quasiconvex() and not lhs.is_convex():
# quasiconvex <= constant
assert rhs.is_constant(), rhs
if inverse.invertible(lhs):
# Apply inverse to both sides of constraint.
rhs = inverse.inverse(lhs)(rhs)
idx = lhs._non_const_idx()[0]
expr = lhs.args[idx]
if lhs.is_incr(idx):
return self._canonicalize_constraint(expr <= rhs)
assert lhs.is_decr(idx)
return self._canonicalize_constraint(expr >= rhs)
elif isinstance(lhs, (maximum, max_atom)):
# Lower maximum.
return [
c for arg in lhs.args
for c in self._canonicalize_constraint(arg <= rhs)
]
else:
# Replace quasiconvex atom with a sublevel set.
canon_args, aux_args_constr = self._canon_args(lhs)
sublevel_set = sets.sublevel(lhs.copy(canon_args), t=rhs)
return sublevel_set + aux_args_constr
# constant <= quasiconcave
assert rhs.is_quasiconcave()
assert lhs.is_constant()
if inverse.invertible(rhs):
# Apply inverse to both sides of constraint.
lhs = inverse.inverse(rhs)(lhs)
idx = rhs._non_const_idx()[0]
expr = rhs.args[idx]
if rhs.is_incr(idx):
return self._canonicalize_constraint(lhs <= expr)
assert rhs.is_decr(idx)
return self._canonicalize_constraint(lhs >= expr)
elif isinstance(rhs, (minimum, min_atom)):
# Lower minimum.
return [
c for arg in rhs.args
for c in self._canonicalize_constraint(lhs <= arg)
]
else:
# Replace quasiconcave atom with a superlevel set.
canon_args, aux_args_constr = self._canon_args(rhs)
superlevel_set = sets.superlevel(rhs.copy(canon_args), t=lhs)
return superlevel_set + aux_args_constr