[Ipopt] non-convex model in IPOPT

[Hossein Haghighat]

Hello all,
Many thanks for reply.
it is a problem of minimum operating cost, in the context of electricity
market.
- F(x,y) is the cost of power, and "mu" is the nodal price in the market
(Lagrange multiplier of the equality constraints ), and y is the power
produced in the market.
- "mu * y" represent the cost of power.

the point is that "mu" is only available post solution, but here it appears
in the objective function.
this problem seems to be non-convex because it entails the product of
variables, and I am not sure if it can be converted into a convex form (if
any).

Writing the optimality conditions is a good way, but we should note that
they are stationary points (saddle-points + local optima)

Your comments are highly appreciated.



On Tue, Jul 26, 2011 at 9:36 PM, 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.
> >
> > _______________________________________________
> > Ipopt mailing list
> > Ipopt at list.coin-or.org
> > http://list.coin-or.org/mailman/listinfo/ipopt
> >
> >
>



-- 
regards,
Hossein.
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