ROI_solve function

Solve an Optimization Problem

Solve a given optimization problem. This function uses the given solver (or searches for an appropriate solver) to solve the supplied optimization problem.

ROI_solve(x, solver, control = list(), ...)

Arguments

• x: an optimization problem of class "OP".
• solver: a character vector specifying the solver to use. If missing, then the default solver returned by ROI_options is used.
• control: a list with additional control parameters for the solver. This is solver specific so please consult the corresponding documentation.
• ...: a list of control parameters (overruling those specified in control).

Returns

a list containing the solution and a message from the solver.

• solutionthe vector of optimal coefficients
• objvalthe value of the objective function at the optimum
• statusa list giving the status code and message form the solver. The status code is 0 on success (no error occurred) 1 otherwise.
• messagea list giving the original message provided by the solver.

Examples

## Rosenbrock Banana Function
## -----------------------------------------
## objective
f <- function(x) {
   return( 100 * (x[2] - x[1] * x[1])^2 + (1 - x[1])^2 )
}
## gradient
g <- function(x) {
   return( c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
             200 * (x[2] - x[1] * x[1])) )
}
## bounds
b <- V_bound(li = 1:2, ui = 1:2, lb = c(-3, -3), ub = c(3, 3))
op <- OP( objective = F_objective(f, n = 2L, G = g),
          bounds = b )
res <- ROI_solve( op, solver = "nlminb", control = list(start = c( -1.2, 1 )) )
solution( res )
## Portfolio optimization - minimum variance
## -----------------------------------------
## get monthly returns of 30 US stocks
data( US30 )
r <- na.omit( US30 )
## objective function to minimize
obj <- Q_objective( 2*cov(r) )
## full investment constraint
full_invest <- L_constraint( rep(1, ncol(US30)), "==", 1 )
## create optimization problem / long-only
op <- OP( objective = obj, constraints = full_invest )
## solve the problem - only works if a QP solver is registered
## Not run:

res <- ROI_solve( op )
res
sol <- solution( res )
names( sol ) <- colnames( US30 )
round( sol[ which(sol > 1/10^6) ], 3 )
## End(Not run)

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