Lui,

you can also have a look at
http://aqr.activequant.org/index.php/2010/08/genetically-optimizing-a-trading-system/for
inspiration on how to genetically optimize a trading system, whether
it's quadratic or not. It's just some snipplet but exemplifies it pretty
well ...

Regards,
Ulrich


On Sun, Jan 23, 2011 at 11:15 PM, Guillaume Yziquel <
guillaume.yziquel@citycable.ch> wrote:

> Le Sunday 23 Jan 2011 à 15:56:40 (-0600), Brian G. Peterson a écrit :
> > On Saturday, January 22, 2011 04:33:09 pm Lui ## wrote:
> > > Dear group,
> > >
> > > I was just wondering whether some of you have some experience with the
> > > package "rgenoud" which does provide genetic algorithms for complex
> > > optimization problems.
> >
> > <...>
> >
> > > What is your general experience? Did you ever try solving the
> > > Markowitz portfolio with the rgenoud package?
> > > I know that there are good solvers around for the qudratic programming
> > > problem of the markowitz portfolio, but I want to go into a different
> > > direction which translates into a quadratic problem with quadratic
> > > constraints (and I havent found a good solver for that...).
> > >
> > > I am interested in your replies! Have a good weekend!
> >
> > As others have already said, for a quadtratic problem with quadratic
> > constraints, there is an exact analytical solution.
>
> I wouldn't qualify dual interior point methods as an "exact" solution, but,
> yes, that's the basic idea: they're better suited for that.
>
> > In these cases, you will be much better off both from a performance and
> > accuracy perspective in using a quadratic solver (quadprog is most often
> > applied in R, see list archives and many packages for examples).
>
> Is quadprog a second-order cone programming solver? If that is the case,
> yes, it probably solves quadratic objective function with quadratic
> constraints faster and with more accuracy than a full-fledged SDP
> solver.
>
> > Other portfolio problems may be stated in terms of linear solvers, which
> will
> > likewise be faster than a global optimizer for finding an exact
> analytical
> > solution.
> >
> > If, however, your portfolio problem is non-convex and non-smooth, then a
> > genetic algorithm, a migration algorithm, grid search, or random
> portfolios
> > may be a good option for finding a near-optimal portfolio.  If this is
> your
> > true goal, perhaps you can say a little more about your actual
> constraints and
> > objectives (and use assets that are outside of your true area of
> interest,
> > such as the S&P sector indices).
>
> Yes, the problem structure often gives good insight as to which method
> to apply. It may be noted, however, that quite a lot of non-convex
> problems may be transformed into convex ones. And using some relaxation
> methods, you can often use SDPs to optimise multivariate polynomial
> objective under multivariate polynomial constraints, without too many
> convexity hypothesis.
>
> SDPs are not always easy to manipulate, but they do solve a broad range
> of optimisation problems.
>
> > Regards,
> >
> >   - Brian
>
> Best regards,
>
> --
>     Guillaume Yziquel
> http://yziquel.homelinux.org
>
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>



-- 
Ulrich Staudinger
https://www.xing.com/profile/Ulrich_Staudinger

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