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Re: Perhaps a FindMinimum issue...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112689] Re: Perhaps a FindMinimum issue...
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Mon, 27 Sep 2010 05:46:08 -0400 (EDT)
  • References: <i7mq2n$oud$1@smc.vnet.net>

>From the manual: "Except when f and cons are both linear, the results
found by FindMinimum may correspond only to local, but not global,
minima. "

If Minimize is too slow for you you might try NMinimize. It has
various methods that you could try.

Cheers -- Sjoerd


On Sep 26, 8:43 am, mpolko lokta <mpolkolo... at gmail.com> wrote:
> I have been trying to:
>
> min 1/2*Transpose[w].V.w,
>
> subject to the constraints
>
> Total[w] == 1
>
> and
>
> Thread[w >= conformable vector of zeros]
>
> for a number of different V matrices using FindMinimum.
>
> One common feature of all the optimization problems I was trying to
> solve is that V was always singular. The dimensions of the V matrix
> ranged from 50 - 250 items.
>
> The problem I am facing is that FindMinimum returns consistently
> suboptimal results.
>
> A hint about that was that some of the lagrange multipliers
> corresponding to the non-negativity constraints I calculated using the
> proposed solution from FindMinimum and the first order conditions of
> the Lagrangean of the optimization problem were actually negative
> (they should have been positive or zero). Some of the negative
> multipliers could be chopped (using Chop[] with default options) to
> zero but others still persisted.
>
> To make sure that I was actually getting suboptimal results that were
> not due to rounding errors etc. I used a number of oher software that
> provided routines for solving constrained quadratic programming
> problems (both proprietary and open source) to solve a small subset of
> the original problems Mathematica was supposedly providing me with
> suboptimal results.
>
> Unfortunately, I verified that FindMinimum was actually producing
> suboptimal results!
>
> After that comparison I tried using Minimize on a small subset of the
> initial problems and I got results that were "closer" to the "right"
> results provided by the other QP solvers, although Minimize's
> solutions were still less than optimum. Another drawback of using
> Minimize was the time it needed to provide an answer.
>
> Does anybody know if the behavior of FindMinimum is due to the
> singularity of the V matrix and has anybody any suggestion on how to
> speed up the time it takes for Minimize to converge?
>
> Thanks!



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