# Domain constraints¶

Optunity supports domain constraints on the objective function. Domain constraints are used to enforce solvers to remain within a prespecified search space. Most solvers that Optunity provides are implicitly unconstrained (cfr. Solver overview), though hyperparameters are usually constrained in some way (ex: regularization coefficients must be positive).

A set of simple constraints and facilities to use them are provided in Domain constraints. Specifically, the following constraints are provided:

• lb_{oc}: assigns a lower bound (open or closed)
• ub_{oc}: assigns an upper bound (open or closed)
• range_{oc}{oc}: creates a range constraint (e.g. $$A < x < B$$)

All of the above constraints apply to a specific hyperparameter. Multidimensional constraints are possible, but you would need to implement them yourself (see Implementing custom constraints).

Note that the functions optunity.maximize() and optunity.minimize() wrap explicit box constraints around the objective function prior to starting the solving process. The expert function optunity.optimize() does not do this for you, which allows more flexibility at the price of verbosity.

Constraint violations in Optunity raise a ConstraintViolation exception by default. The usual way we handle these exceptions is by returning a certain (typically bad) default function value (using the optunity.constraints.violations_defaulted() decorator). This will cause solvers to stop searching in the infeasible region.

To add a series of constraints, we recommend using the optunity.wrap_constraints() function. This function takes care of assigning default values on constraint violations if desired.

## Implementing custom constraints¶

Constraints are implemented as a binary functions, which yield false in case of a constraint violation. You can design your own constraint according to this principle. For instance, assume we have a binary function with two arguments x and y:

def f(x, y):
return x + y


Optunity provides all univariate constraints you need, but lets say we want to constrain the domain to be the unit circle in x,y-space. We can do this using the following constraint:

constraint = lambda x, y: (x ** 2 + y ** 2) <= 1.0


To constrain f, we use optunity.wrap_constraints():

fc = optunity.wrap_constraints(f, custom=[constraint])


The constrained function fc(x, y) will yield x + y if the arguments are within the unit circle, or raise a ConstraintViolation exception otherwise.