Refactor CMP and CMPState

[merajhashemi]

CMP and CMPState

• Converted CMPState into a dataclass for improved readability and maintainability.
• Removed dual attributes from LagrangianStore.
• Moved the backward method from CMPState to LagrangianStore.
• Utilized LagrangianStore as a data structure to organize information within CMPState replacing direct attributes such as self.lagrangian and self.dual_lagrangian.
• Added constraints attribute and related helper methods to CMP
• Renamed populate_lagrangian to compute_lagrangian method
• Removed purge_* methods for lagrangians
• Added dual_parameters() method for fetching multiplier parameters for instantiating the dual optimizer

PenaltyCoefficients

• Transformed PenaltyCoefficients to no longer be nn.module.
• Wrapped __call__ in no_grad mode for efficiency.
• Implemented def __call__(self, *args, **kwargs): in the base class for consistency.
• Adjusted __call__ to return cloned values.
• Moved penalty coefficient update parameters out of Formulation and into PenaltyCoefficientUpdater.
• Introduced PenaltyCoefficientUpdater to handle update schemes for penalty coefficients.
• Implemented Multipicative

Updates from #88

Constraint

• Extracted ConstraintType enum to separate module to resolve circular dependency issues between Constraint, Formulation and Multiplier.

Formulations

• Removed PenaltyFormulation and QuadraticPenaltyFormulation
  • PenaltyFormulation is deprecated in favor of asking users to formulate penalized tasks directly through their objective function
  • We retain some utility functions for the QuadraticPenaltyFormulation. We will add a tutorial to illustrate the use of a Quadratic Penalty formulation in Cooper.
• Only LagrangianFormulation and AugmentedLagrangianFormulation remain. Now it is mandatory to provide a Multiplier when building a formulation.
• Removed FormulationType.
• Removed formulation kwargs such as penalty_growth_factor and violation_tolerance.

Multipliers

• Now expect init tensor (if provided) to have shape (num_constraints,). Else, num_constraints:int is expected and we initialize the multipliers with zeros of shape (num_constraints,).
• Removed support for dual_restarts.
• Refactored enforce_positive attribute to is_inequality property.
• Gathered equality and inequality multiplier tests into joint tests for ExplicitMultipliers

Updates from #89

• Changed observed_constraints attribute of CMPState to be a dictionary with Constraint keys and ConstraintState values
• Similarly, refactored constraint_measurements to be a dictionary with Constraint keys and ConstraintMeasurement values
• Added utility function for retrieving observed_multiplier_values from LagrangianStore
• Added utility function for retrieving observed_violations and observed_violations from CMPState

Updates from #90

• Implement CooperOptimizer abstract base class
  • Both ConstrainedOptimizer and UnconstrainedOptimizer inherit from CooperOptimizer
• Add RollOut for organizing returns of roll method
• Remove ConstraintMeasurement
• Add ContributionStore
• Remove AugmentedLagrangian optimizers
• Fix Penalty Coefficient and Updater to allow for scalar values
• Remove Slacks