[Ipopt] Ipopt Digest, Vol 114, Issue 7

[Damien]

Thanks.  I had a separate conversation with Carl Laird, and his 
recommendation was to keep the variables in the objective.  We only 
discussed smooth problems and no corner cases.  Carl said that even 
though the objective is part of the Lagrangian and so any variable and 
constraint changes in there should be equivalent, in his experience 
Ipopt performs better with the variables in the objective, based on how 
the line search works.

Damien

On 2014-06-13 11:02 AM, Andrew R Conn wrote:
> <<Mathematically (and I think algorithmically) these are equivalent
>
> Not necessarily. Depends very much on the context
>
> eg
>
> min_x max_i f_i(x)
>
> is non-smooth
>
> cf with
>
> min_x,z z
>
> subject to  z>= f_i(x)
>
> for an example
>
>
> Andrew R. Conn
> BM T. J. Watson Research Center
>
>
>
> From: ipopt-request at list.coin-or.org
> To: ipopt at list.coin-or.org,
> Date: 06/13/2014 12:03 PM
> Subject: Ipopt Digest, Vol 114, Issue 7
> Sent by: ipopt-bounces at list.coin-or.org
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> Today's Topics:
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>   1. Re: question on formulation of the objective function and
>      IPOPT performance (Greg Horn)
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> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 13 Jun 2014 14:36:51 +0200
> From: Greg Horn <gregmainland at gmail.com>
> To: Damien <damien at khubla.com>
> Cc: ipopt mailing list <ipopt at list.coin-or.org>
> Subject: Re: [Ipopt] question on formulation of the objective function
> and IPOPT performance
> Message-ID:
> <CAAr-h4v3uuR=cHmXqgNbBSXO_v4PGE7aLNGg8qdn+S1sTFvsPg at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hi Damien,
>
> Since no one has answered I'll take a shot at it, though it's not my
> expertise. The case you described is:
>
> minimize f(x) w.r.t {x}
> vs
> minimize y w.r.t {x,y}, subject to y == f(x)
>
> I'm not sure if there will be any difference in this case. However, I have
> had personal experience with:
>
> minimize f(g(x)) w.r.t {x}      [prob1]
> vs
> minimize f(y) w.r.t. {x, y} subject to y == g(x)    [prob2]
>
> In this case you can have significantly better convergence by "lifting"
> these variables out. [prob2] will compute a better search direction than
> [prob1]. This is why people use direct multiple shooting instead of direct
> single shooting sometimes. There are even specialized lifting solvers 
> which
> can do linear algebra in the space of [prob1] and obtain the search
> direction in the space of [prob2], for example:
> http://num.math.uni-bayreuth.de/en/conferences/ompc_2013/program/download/friday/Diehl_ompc2013.pdf
>
> Hope this helps,
> Greg
>
>
> On Wed, Jun 11, 2014 at 8:52 PM, Damien <damien at khubla.com> wrote:
>
> > All,
> >
> > I'm looking at two ways to formulate the objective function in a new
> > optimisation model.  The first way is what you'd call the 
> conventional way
> > I suppose, where you have a variety of variables contributing to the
> > objective value and you calculate the gradient and return that to IPOPT.
> >  The other way I'm considering is to equate the objective function 
> to a new
> > variable in an extra equality constraint, and have the new variable 
> as the
> > only variable in the objective, with a gradient of 1.0.  The new 
> equality
> > constraint then contributes first partial derivatives like any other
> > equation or constraint.
> >
> > Mathematically (and I think algorithmically) these are equivalent, but I
> > was wondering if anyone who's done this before has seen a performance
> > difference between the two.
> >
> > Cheers,
> >
> > Damien
> > _______________________________________________
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> > http://list.coin-or.org/mailman/listinfo/ipopt
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