ROI (version 0.2-1)

OP: Optimization Problem Constructor

Description

Optimization problem constructor

Usage

OP(objective, constraints = NULL, types = NULL, bounds = NULL, 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.

Value

A list containing the optimal solution, with the following components.

solution

the vector of optimal coefficients

objval

the value of the objective function at the optimum

status

an integer with status information about the solution returned: 0 if the optimal solution was found, a non-zero value otherwise

msg

the status code and additional information about the solution provided by the solver.

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