Example-2 {ROI.plugin.scs}

SOCP 2

Description

The following example is also known as Problem 10 from the Hock-Schittkowski-Collection Hock and Schittkowski (1981).

minimize \ \ x - y \\

subject \ to \ \ -3 x^2 + 2 x y + 1 \geq 0

References

W. Hock, K. Schittkowski (1981): Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer

Examples

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

obj <- L_objective(c(1, -1))
L <- chol(rbind(c(3, -1), c(-1, 1)))
con <- C_constraint(L = rbind(0, -L), cones = K_soc(3), rhs = c(1, 0, 0))
op <- OP(objective = obj, constraints = con, 
         bounds = V_bound(li = 1:2, lb = rep(-Inf, 2)))
x <- ROI_solve(op, solver="scs")
x
## Optimal solution found.
## The objective value is: -1.000000e+00
solution(x)
## [1] 1.996387e-10 1.000000e+00