scs_quadratic_program.jl

using JuMP
using SCS
using Gurobi

# Objective is min. 1/2 x'Qx + q'x
Q = [1 0.1; 0.1 1]
q = [-3., 4]

## Solve with SCS
m = Model(solver=SCSSolver())
@variable m x[1:2]
@constraint m x[1] >= 1
@constraint m x[2] >= 1.5

# trick from http://www.seas.ucla.edu/~vandenbe/publications/socp.pdf
@variable m slack >= 0
P = sqrtm(Q)
@constraint m norm(P * x + P \ q) <= slack
@objective m Min slack
solve(m)
getvalue(x)

## Solve with Gurobi
m = Model(solver=GurobiSolver())
@variable m x[1:2]
@objective m Min (x' * Q * x)[1] + 2 * (q' * x)[1]
@constraint m x[1] >= 1
@constraint m x[2] >= 1.5
solve(m)
getvalue(x)