Hi, now the EXIT: Restoration Failed issue was gone, but I am having strange optimal solution with the following example

**using JuMP**

**using Ipopt**

model = Model(Ipopt.Optimizer)

@variable(model, α, start=1.0 )

@variable(model, β, start=1.0 )

x = [1. 2.; 3. -1; 5.0 3.;6. 7.]

f(α, β) = maximum(sum([α β] .* x, dims=2))

g(α, β) = minimum(sum([α β] .* x, dims=2))

JuMP.register(model, :f, 2, f, autodiff=true)

JuMP.register(model, :g, 2, g, autodiff=true)

@NLobjective(model, Max, f(α, β) / g(α, β) )

optimize!(model)

**output**

Number of objective function evaluations = 368

Number of objective gradient evaluations = 12

Number of equality constraint evaluations = 0

Number of inequality constraint evaluations = 0

Number of equality constraint Jacobian evaluations = 0

Number of inequality constraint Jacobian evaluations = 0

Number of Lagrangian Hessian evaluations = 0

Total CPU secs in IPOPT (w/o function evaluations) = 0.171

Total CPU secs in NLP function evaluations = 0.004

EXIT: Optimal Solution Found.

**result:**

julia> value(α)

-6.616112462703816e14

julia> value(β)

2.2053711899565838e14

julia> objective_value(model)

0.08333330892901637

however, this is definitely not good solution as even with start number 1, the objective could be 6.5. what is wrong with my formulation?