Adding the unbalanced penalization method

Following recent thread about the unbalanced penalization equation to encode inequality constraints. dwavesystems#1339

dimod/binary/binary_quadratic_model.py

@@ -703,12 +703,13 @@ def add_linear_equality_constraint(
 
  def add_linear_inequality_constraint(
  self, terms: Iterable[Tuple[Variable, int]],
- lagrange_multiplier: Bias,
+ lagrange_multiplier: Union[Bias, Iterable],
  label: str,
  constant: int = 0,
  lb: int = np.iinfo(np.int64).min,
  ub: int = 0,
- cross_zero: bool = False
+ cross_zero: bool = False,
+ penalization_method: str = "slack"
  ) -> Iterable[Tuple[Variable, int]]:
  """Add a linear inequality constraint as a quadratic objective.
 
@@ -739,6 +740,10 @@ def add_linear_inequality_constraint(
  Upper bound for the constraint.
  cross_zero:
  When True, adds zero to the domain of constraint.
+ penalization_method:
+ Whether to use slack variables or the unbalanced penalization method [1].
+ ("slack", "unbalanced")
+ [1] https://arxiv.org/abs/2211.13914
 
  Returns:
  slack_terms: Values of :math:`\sum_{i} b_{i} slack_{i}` as an
@@ -772,35 +777,41 @@ def add_linear_inequality_constraint(
  raise ValueError(
  f'The given constraint ({label}) is infeasible with any value'
  ' for state variables.')
-
- slack_upper_bound = int(ub_c - lb_c)
- if slack_upper_bound == 0:
- self.add_linear_equality_constraint(terms, lagrange_multiplier, -ub_c)
+ if penalization_method == "slack":
+ slack_upper_bound = int(ub_c - lb_c)
+ if slack_upper_bound == 0:
+ self.add_linear_equality_constraint(terms, lagrange_multiplier, -ub_c)
+ return []
+ else:
+ slack_terms = []
+ zero_constraint = False
+ if cross_zero:
+ if lb_c > 0 or ub_c < 0:
+ if ub_c-slack_upper_bound > 0:
+ zero_constraint = True
+
+ num_slack = int(np.floor(np.log2(slack_upper_bound)))
+ slack_coefficients = [2 ** j for j in range(num_slack)]
+ if slack_upper_bound - 2 ** num_slack >= 0:
+ slack_coefficients.append(slack_upper_bound - 2 ** num_slack + 1)
+
+ for j, s in enumerate(slack_coefficients):
+ sv = self.add_variable(f'slack_{label}_{j}')
+ slack_terms.append((sv, s))
+
+ if zero_constraint:
+ sv = self.add_variable(f'slack_{label}_{num_slack + 1}')
+ slack_terms.append((sv, ub_c - slack_upper_bound))
+
+ self.add_linear_equality_constraint(terms,lagrange_multiplier[0], -ub_c)
+
+ return slack_terms
+
+ elif penalization_method == "unbalanced":
+ self.add_linear_equality_constraint(terms,lagrange_multiplier[0], -ub_c)
+ for v, bias in terms:
+ self.add_linear(v, -lagrange_multiplier[1] * bias)
  return []
- else:
- slack_terms = []
- zero_constraint = False
- if cross_zero:
- if lb_c > 0 or ub_c < 0:
- if ub_c-slack_upper_bound > 0:
- zero_constraint = True
-
- num_slack = int(np.floor(np.log2(slack_upper_bound)))
- slack_coefficients = [2 ** j for j in range(num_slack)]
- if slack_upper_bound - 2 ** num_slack >= 0:
- slack_coefficients.append(slack_upper_bound - 2 ** num_slack + 1)
-
- for j, s in enumerate(slack_coefficients):
- sv = self.add_variable(f'slack_{label}_{j}')
- slack_terms.append((sv, s))
-
- if zero_constraint:
- sv = self.add_variable(f'slack_{label}_{num_slack + 1}')
- slack_terms.append((sv, ub_c - slack_upper_bound))
-
- self.add_linear_equality_constraint(terms + slack_terms,
- lagrange_multiplier, -ub_c)
- return slack_terms
 
  def add_linear_from_array(self, linear: Sequence):
  """Add linear biases from an array-like to a binary quadratic model.