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!