Add constraints to an lp_problem() — lp

Restrict the variables in an lp_problem() with linear constraints.

Usage

lp_constraint(.problem, ...)

lp_con(.problem, ...)

lp_subject_to(.problem, ...)

Arguments

.problem

An lp_problem().

...

One or more linear constraints. Can be named. They must:

Contain one or more variables defined with lp_variable()
Contain a comparison operator ( < / <= / == / => / > )

Value

The .problem with added $constraints. (Note: previous constraints are not overritten).

Constraints can be represented as lhs * vars <dir> rhs.

The $constraints field has the following subfields:

$lhs : slam::simple_triplet_matrix() where each row is a constraint, each column is a variable, and the values represent coefficients.
$dir : Character vector with elements "<=", "==", or ">=", the direction of each constraint.
$rhs : Numeric column vector representing the right hand side of each constraint.
$name : Character vector with the names of the constraints, if ... is named, or "" for unnamed constraints.
$call : Expression that defined each constraint.

Examples

# Ordered variable constraint
## ordered[i] > ordered[i-1]  for all i in 2:n
n <- 4
p <- lp_problem() |>
    lp_variable(ordered[1:n], lower = 0)

## Three alternatives
pc <- p |> lp_constraint(
    alt1 = ordered[2:n] > ordered[1:(n-1)],
    alt2 = for (i in 2:n) ordered[i] > ordered[i-1]
)

## The 'for' construct can be wrapped around 'lp_constraint' instead of inside it
for (i in 2:n) {
    pc <- pc |> lp_constraint(
        alt3 = ordered[i] > ordered[i-1]
    )
}

## The only difference are the rownames of the constraint matrix
print(pc$constraints)
#> 
#>  alt1 | n = 3 | ordered[2:n] > ordered[1:(n - 1)]
#> 
#>      ordered[1] ordered[2] ordered[3] ordered[4] dir  
#> alt1 -1         1          0          0          >=  0
#> alt1 0          -1         1          0          >=  0
#> alt1 0          0          -1         1          >=  0
#> 
#> 
#>  alt2 | n = 3 | for (i in 2:n) ordered[i] > ordered[i - 1]
#> 
#>           ordered[1] ordered[2] ordered[3] ordered[4] dir  
#> alt2[i=2] -1         1          0          0          >=  0
#> alt2[i=3] 0          -1         1          0          >=  0
#> alt2[i=4] 0          0          -1         1          >=  0
#> 
#> 
#>  alt3 | n = 3 | ordered[i] > ordered[i - 1]
#> 
#>      ordered[1] ordered[2] ordered[3] ordered[4] dir  
#> alt3 -1         1          0          0          >=  0
#> alt3 0          -1         1          0          >=  0
#> alt3 0          0          -1         1          >=  0
#>