# Unable to transform a quadratic constraint into a second-order cone constraint because the quadratic constraint is not strongly convex
**URL:** https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767
**Category:** Optimization (Mathematical)
**Created:** [April 21, 2022, 7:50am UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767 "2022-04-21T07:50:46Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Eric.O](https://discourse.julialang.org/u/Eric.O)
#### Post date: [April 21, 2022, 7:50am UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767/1 "2022-04-21T07:50:46Z")
I am using Mosek solver to solve the model below. I get the model showing but the solver is not able to display the results. Am guessing is an issue with the second order cone formulation. I will appreciate your guidance to get this working please.
using JuMP
using Mosek
using MosekTools
model= Model(Mosek.Optimizer)
# Let parameter
m=15
NumVar=5
r=[0, 0, 0, 0, 0]
@variable(model, X\>=0)
@variable(model, y\>=0)
@variable(model, z\>=0)
@variable(model, a[i=1:NumVar]\>=0)
@variable(model, b[i=1:NumVar]\>=0)
@variable(model, R\>=0)
######
@objective(model, Min, X^2 + y^2-z )
#######Declare the constraints
for i in 1:NumVar
@constraint(model, -2_X_a[i]-2\*b[i]\*y + z \<=(R-r[i])^2-a[i]^2-b[i]^2)
end
@show model
print(model)
optimize!(model)
@show termination\_status(model)
@show primal\_status(model)
@show dual\_status(model)
@show objective\_value(model)
for i in 1:NumVar
println("r[$i] = ", value(r[i]))
end
@show value(X)
@show value(y)
@show value(R)
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 21, 2022, 8:18am UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767/2 "2022-04-21T08:18:33Z")
Mosek is a conic solver, so it requires that your problem formulation is convex. Your problem is non-convex because it has bilinear terms. like `X * a[i]`.
If you expected your problem to be convex, you should take another look at the formulation. Otherwise you could try a solver like Ipopt that can find locally optimal solutions to non-convex problems, or Gurobi, which can solve this problem to global optimality.
---
### Author:  [@Eric.O](https://discourse.julialang.org/u/Eric.O)
#### Post date: [April 21, 2022, 8:46am UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767/3 "2022-04-21T08:46:53Z")
Is there a way I can reformulate my non convex model to be convex or unless I get a solver that can solve non covex problem like you said earlier.
Do I need a license before using Gurobi?
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [April 21, 2022, 9:04am UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767/4 "2022-04-21T09:04:30Z")
No, you typically can’t reformulate nonconvex problems to be convex
And yes, Gurobi is commercial, but they have free licenses for academics.
---
### Author:  [@Eric.O](https://discourse.julialang.org/u/Eric.O)
#### Post date: [April 21, 2022, 1:13pm UTC](https://discourse.julialang.org/t/unable-to-transform-a-quadratic-constraint-into-a-second-order-cone-constraint-because-the-quadratic-constraint-is-not-strongly-convex/79767/5 "2022-04-21T13:13:38Z")
Thank you very much