@dpo : this is right : my constraints are linear and my objective function is quadratic.

Here is the minimal working example

```
using LinearAlgebra
using JuMP
using COSMO
X=[1 1; 1 2; 2 2 ];
y=[+1 -1 -1 ];
n=length(y);
p=size(X,2);
G=X*X';
model = Model(with_optimizer(COSMO.Optimizer))
@variables model begin
alpha[i=1:length(y)]
end
@NLobjective(model, Min, sum(0.5*alpha[k]*G[k,i]*y[k]*y[i]*alpha[i] -alpha[k] for i=1:n for k=1:n))
@constraint(model, sum( y[i] * alpha[i] for i=1:n ) == 0)
@constraint(model, [i=1:n], -alpha[i]<=0)
optimize!(model);
alpha_opt = value.(alpha);
```

And here is the output I get :

julia> optimize!(model);

```
COSMO v0.5.0 - A Quadratic Objective Conic Solver
Michael Garstka
University of Oxford, 2017 - 2019
```

Problem: x ∈ R^{3},

constraints: A ∈ R^{4x3} (6 nnz),

matrix size to factor: 7x7 (19 nnz)

Sets: Nonnegatives of dim: 3

ZeroSet of dim: 1

Settings: ϵ_abs = 1.0e-04, ϵ_rel = 1.0e-04,

ϵ_prim_inf = 1.0e-06, ϵ_dual_inf = 1.0e-04,

ρ = 0.1, σ = 1.0e-6, α = 1.6,

max_iter = 2500,

scaling iter = 10 (on),

check termination every 40 iter,

check infeasibility every 40 iter,

KKT system solver: QDLDL

Setup Time: 1967.41ms

Iter: Objective: Primal Res: Dual Res: Rho:

40 0.0000e+00 0.0000e+00 0.0000e+00 1.0000e-01

Results

Status: Solved

Iterations: 40

Optimal objective: 0.0

Runtime: 2.754s (2754.23ms)

julia> alpha_opt = value.(alpha)

3-element Array{Float64,1}:

0.0

0.0

0.0

I was expecting julia to give me this solution : [2 ,2 ,0].