Hi all,

I am using Couenne for my MINLP problem. I have a problem using Couenne when I add a nonlinear term to the objective. I have tried different options in the couenne.opt file based on different posts here, still no results (Clp0000I Optimal - objective value 0). Here is a simple version of my code with only the problematic objective function:

using JuMP

using AmplNLWriter

```
m = Model(with_optimizer(AmplNLWriter.Optimizer, "path to couenne.exe"))
#m = Model(with_optimizer(Ipopt.Optimizer))
min_velocity = 0.6
max_velocity = 1.5
nu = 1e-6
g = 9.81
rho = 1000
pump_efficiency = 0.6
Cost_per_kWh = 0.24 #Dollars/kWh
pipe_roughness = 0.00015
Di_standard = 1e-3*[0; 32; ;40 ; 50; 63; 75; 90; 110; 125; 140; 160; 180; 200; 225; 250]
Price_per_Unit_pipe = [0; 1.08; 1.72; 2.65; 4.22; 5.95; 8.56; 12.74; 16.25; 20.40; 26.51; 33.68; 41.56; 52.71; 64.60]
QP = [0.06, 0.04]
Dis = [20 100; 100 20]
NP = size(QP,1) # number of units
NDi = size(Di_standard,1) # number of available standard diameters
@variable(m, x[1:NP, 1:NP] >= 0)
@variable(m, Di[1:NP, 1:NP] >= 0)
@variable(m, QFW[1:NP] >= 0)
@variable(m, v[1:NP, 1:NP] >= 0)
@variable(m, 0 <= Re[1:NP, 1:NP])
@variable(m, 0 <= f[1:NP, 1:NP])
@variable(m, 0 <= hf[1:NP, 1:NP])
@variable(m, Di_idx[1:NP, 1:NP, 1:NDi], Bin)
@variable(m, x_idx[1:NP, 1:NP], Bin)
@constraint(m, 0 .<= QP - x'*QP)
@constraint(m, 1 .>= sum(x, dims=2))
@constraint(m, 1 .== sum(Di_idx, dims=3))
@constraint(m, [i = 1:NP, j = 1:NP], Di[i,j] == sum(Di_standard[n]*Di_idx[i,j,n] for n = 1:NDi))
@constraint(m, [i = 1:NP, j = 1:NP], QFW[i] == QP[i] - sum(x[j,i]*QP[j] for j = 1:NP))
@constraint(m, sum(QFW[i] for i =1:NP)/sum(QP[i] for i = 1:NP) == 0.2)
@NLconstraint(m, [i = 1:NP, j = 1:NP], v[i,j] == 4*x[i,j]*QP[i]/(pi*Di[i,j]*Di[i,j]))
#Big-M formulation
@constraint(m, x .<= x_idx)
@constraint(m, x .>= 0)
@variable(m, Di_aux[1:NP, 1:NP])
@constraint(m, Di - Di_aux .<= (1-x_idx))
@constraint(m, 0 .<= Di - Di_aux)
@constraint(m, 0 .<= Di_aux )
@constraint(m, Di_aux .<= x_idx)
M1 = 10
@variable(m, v_aux[1:NP, 1:NP])
@constraint(m, v - v_aux .<= M1*(1-x_idx))
@constraint(m, 0 .<= v - v_aux)
@constraint(m, min_velocity*x_idx .<= v_aux )
@constraint(m, v_aux.<= max_velocity*x_idx)
@NLconstraint(m, [i = 1:NP, j = 1:NP], Re[i,j] == Di[i,j]*v[i,j]/nu)
@NLconstraint(m, [i = 1:NP, j = 1:NP], f[i,j] == 0.316/(Re[i,j]^0.25)*x_idx[i,j])
@variable(m, f_aux[1:NP, 1:NP])
@constraint(m, f- f_aux .<= (1-x_idx))
@constraint(m, 0 .<= f - f_aux)
@constraint(m, 0 .<= f_aux)
@constraint(m, f_aux .<= x_idx)
M2 = 10
@NLconstraint(m, [i = 1:NP, j = 1:NP], hf[i,j] == (f[i,j]/Di[i,j])*Dis[i,j]*(v[i,j]^2/(2*g))) # Darcy equation
@variable(m, hf_aux[1:NP, 1:NP])
@constraint(m, hf- hf_aux .<= M2*(1-x_idx))
@constraint(m, 0 .<= hf - hf_aux)
@constraint(m, 0 .<= hf_aux)
@constraint(m, hf_aux .<= M2*x_idx)
@NLexpression(m, energy_cost[i = 1:NP, j = 1:NP], rho*x[i,j]*QP[i]*hf[i,j]*g/pump_efficiency*Cost_per_kWh/1000)
@NLobjective(m, Min, sum(energy_cost[i,j] for i = 1:NP, j = 1:NP)/sum(QP[i] for i = 1:NP, j = 1:NP))
JuMP.optimize!(m)
```