[Ipopt] non-convex model in IPOPT

[rony goldenthal]

Hello Hossein,

The main challenge in implementing the function in IPOPT, as you
describe it, is that the Lagrange multipliers are not easily available
when evaluating the function to minimize.
Maybe you can try something like adding another set of variables, 'z',
and solve the following system instead:

Min L (x,y,z)= F(x)+ z * y      (a1)
s.t.
g(x,y) = 0                               (a2)
h(x,y)<= 0                              (a3)
z - mu = 0                              (a4)
Where mu are the Lagrange multipliers that correspond to g(x,y).

I cannot say much about the convexity of either of the approaches.

Good luck,
Rony

On Mon, Jul 25, 2011 at 9:00 PM, Hossein Haghighat
<hosein.haghighat at gmail.com> wrote:
> Hello,
> I was wondering if I can solve a problem in the following form by IPOPT:
>
> Min L (x,y,mu)= F(x)+ mu * y      (a1)
>
> s.t.
>
>
>
> g(x,y) = 0     : mu               (a2)
>
> h(x,y)<= 0     : lambda           (a3)
>
> where "mu" is the Lagrange multiplier of equality constraint (a2) appearing
> in the objective function.
> this problem is non-convex. is it true? and can it be solved by IPOPT?
> --
> regards,
> Hossein.
>
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