QCQP problem using Convex.jl

qcqp_convex.jl

## QCQP problem in a convex sub-domain

a = 77.5625
F = [   351.0     26255.2          -6647.07         1282.81
 26255.2         2.23819e6  -780203.0         80689.2 
 -6647.07  -780203.0              1.25858e6  151221.0 
  1282.81    80689.2         151221.0        979604.0]
V = [375.77,11564.5,18360.6,3891.82]

# unconstrained min
xunc = [5.0,-0.05,0.01,0.0]

# constrained min
xtrue = [5.0,-0.0516607,0.00584747,0.000464669]

using Convex, Gurobi

x = Variable(4)
constr = [sqrt(a) * norm(x[3:4]) <= -x[2]]
pr = minimize(sum_squares(F * x - V), constr)
solve!(pr, GurobiSolver())

# pr_unc = minimize(sum_squares(F * x - V))
# solve!(pr_unc, GurobiSolver())

xopt = vec(x.value)

norm(F * xopt - V) 
norm(F * xtrue - V)
# xopt is much smaller

a * xopt[3]^2 + a*xopt[4]^2 <= xopt[2]^2
# True