# Example_03: SOCP 3 In ROI.plugin.scs: 'SCS' Plug-in for the 'R' Optimization Infrastructure

## Description

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

minimize \ \ -2x_1 + x_2 + 5 x_3

subject to

≤ft\| \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 ≤q -12 x_1 - 6 x_2 + 5 x_3 - 12

≤ft\| \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 ≤q -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, http://cvxopt.org/

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 library(ROI) 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="scs") x ## Optimal solution found. ## The objective value is: -3.834637e+01 solution(x) ## [1] -5.014767 -5.766924 -8.521796 

ROI.plugin.scs documentation built on Aug. 30, 2020, 1:06 a.m.