# gurobi_feasrelax()

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### gurobi_feasrelax()

 gurobi_feasrelax ( model, relaxobjtype, minrelax, penalties ) gurobi_feasrelax ( model, relaxobjtype, minrelax, penalties, params )

This function computes a feasibility relaxation for the input model argument. The feasibility relaxation is a model that, when solved, minimizes the amount by which the solution violates the bounds and linear constraints of the original model. You must provide a penalty to associate with relaxing each individual bound or constraint (through the penalties argument). These penalties are interpreted in different ways, depending on the value of the relaxobjtype argument.

Arguments:

model: The model struct must contain a valid Gurobi model. See the model argument section for more information.

relaxobjtype: The approach used to impose penalties on violations.
If you specify relaxobjtype=0, the objective for the feasibility relaxation is to minimize the sum of the weighted magnitudes of the bound and constraint violations.
If you specify relaxobjtype=1, the objective for the feasibility relaxation is to minimize the weighted sum of the squares of the bound and constraint violations.
If you specify relaxobjtype=2, the objective for the feasibility relaxation is to minimize the weighted count of bound and constraint violations.
In all cases, the weights are taken from penalties.lb, penalties.ub and penalties.rhs. You can provide the special penalty value Inf to indicate that the corresponding bound or constraint cannot be relaxed.

minrelax: The minrelax argument is a boolean that controls the type of feasibility relaxation that is created. If minrelax=false, optimizing the returned model gives a solution that minimizes the cost of the violation. If minrelax=true, optimizing the returned model finds a solution that minimizes the original objective, but only from among those solutions that minimize the cost of the violation. Note that gurobi_feasrelax must solve an optimization problem to find the minimum possible relaxation when minrelax=true, which can be quite expensive.

penalties: The penalties argument is a struct array, having the following optional fields (default: all Inf):
lb Penalty for violating each lower bound.
ub Penalty for violating each upper bound.
rhs Penalty for violating each constraint.

To give an example, if a constraint with penalties.rhs value p is violated by 2.0, it would contribute 2*p to the feasibility relaxation objective for relaxobjtype=0, 2*2*p for relaxobjtype=1, and p for relaxobjtype=2.

params: The params struct, when provided, contains a list of modified Gurobi parameters. See the params argument section for more information.

Return value:

A struct containing two fields:
result.model, a struct variable, as described in the model argument section.
result.feasobj, a scalar. If minrelax==true this is the relaxation problem objective value, 0.0 otherwise.

Example usage: