OP function

Optimization Problem Constructor

Optimization problem constructor

OP(objective, constraints, types, bounds, maximum = FALSE)

as.OP(x)

Arguments

• objective: an object inheriting from class "objective".

• constraints: an object inheriting from class "constraints".

• types: a character vector giving the types of the objective variables, with "C", "I", and "B"

  corresponding to continuous, integer, and binary, respectively, or NULL (default), taken as all-continuous. Recycled as needed.

• bounds: NULL (default) or a list with elements upper and lower containing the indices and corresponding bounds of the objective variables. The default for each variable is a bound between 0 and Inf.

• maximum: a logical giving the direction of the optimization. TRUE means that the objective is to maximize the objective function, FALSE (default) means to minimize it.

• x: an R object.

Returns

an object of class "OP".

Examples

## Simple linear program.
## maximize:   2 x_1 + 4 x_2 + 3 x_3
## subject to: 3 x_1 + 4 x_2 + 2 x_3 <= 60
##             2 x_1 +   x_2 +   x_3 <= 40
##               x_1 + 3 x_2 + 2 x_3 <= 80
##               x_1, x_2, x_3 are non-negative real numbers

LP <- OP( c(2, 4, 3),
          L_constraint(L = matrix(c(3, 2, 1, 4, 1, 3, 2, 2, 2), nrow = 3),
                       dir = c("<=", "<=", "<="),
                       rhs = c(60, 40, 80)),
          max = TRUE )
LP

## Simple quadratic program.
## minimize: - 5 x_2 + 1/2 (x_1^2 + x_2^2 + x_3^2)
## subject to: -4 x_1 - 3 x_2       >= -8
##              2 x_1 +   x_2       >=  2
##                    - 2 x_2 + x_3 >=  0

QP <- OP( Q_objective (Q = diag(1, 3), L = c(0, -5, 0)),
          L_constraint(L = matrix(c(-4,-3,0,2,1,0,0,-2,1),
                                  ncol = 3, byrow = TRUE),
                       dir = rep(">=", 3),
                       rhs = c(-8,2,0)) )
QP

References

Theussl S, Schwendinger F, Hornik K (2020). 'ROI: An Extensible R Optimization Infrastructure.' Journal of Statistical Software_, 94(15), 1-64. doi: 10.18637/jss.v094.i15 (URL: https://doi.org/10.18637/jss.v094.i15).

Author(s)

Stefan Theussl