[Ipopt] non-convex model in IPOPT

[Andreas Waechter]

Hi,

You cannot include dual variables (multipliers) into the (primal) problem statement. Both formulations do not make sense (for any optimization algorithm). Not sure what you are trying to model, but you need to find a way to just pose it as a problem where you want to find values of variables that minimize an objective function subject to constraint functions, where all functions depend only on the primal variables. 

Andreas

On Jul 26, 2011, at 13:06, rony goldenthal <ronygold at gmail.com> wrote:

> 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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>> 
>> 
> 
> 
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