Example-3 {ROI.plugin.clarabel}

SOCP 3

Description

The following example is originally from the CVXOPT (https://cvxopt.org/userguide/coneprog.html) homepage.

minimize \ \ -2x_1 + x_2 + 5 x_3

subject to

\left\| \begin{array}{c} -13 x_1 + 3 x_2 + 5 x_3 - 3 \\ -12 x_1 + 12 x_2 - 6 x_3 - 2 \end{array} \right\|_2 \leq -12 x_1 - 6 x_2 + 5 x_3 - 12

\left\| \begin{array}{c} -3 x_1 + 6 x_2 + 2 x_3 \\ x_1 + 9 x_2 + 2 x_3 + 3 \\ - x_1 - 19 x_2 + 3 x_3 - 42 \end{array} \right\|_2 \leq -3 x_1 + 6 x_2 - 10 x_3 + 27

References

Andersen, Martin S and Dahl, Joachim and Vandenberghe, Lieven (2016) CVXOPT: A Python package for convex optimization, version 1.1.8, https://cvxopt.org/

Examples

Sys.setenv("ROI_LOAD_PLUGINS" = FALSE)
library(ROI)
library(ROI.plugin.clarabel)

lo <- L_objective(c(-2, 1, 5))
lc1 <- rbind(c(12, 6, -5), c(13, -3, -5), c(12, -12, 6))
lc2 <- rbind(c(3, -6, 10), c(3, -6, -2), c(-1, -9, -2), c(1, 19, -3))
lc <- C_constraint(L = rbind(lc1, lc2), 
                   cones = K_soc(c(3, 4)), 
                   rhs = c(c(-12, -3, -2), c(27, 0, 3, -42)))
vb <- V_bound(li = 1:3, lb = rep(-Inf, 3))
op <- OP(objective = lo, constraints = lc, bounds = vb)
x <- ROI_solve(op, solver="clarabel")
x
## Optimal solution found.
## The objective value is: -3.834637e+01
solution(x)
## [1] -5.014767 -5.766924 -8.521796