[R-SIG-Finance] DEoptim and guarantees (was: parma - How to optimize a long/short portfolio with sum( abs( weights )) = 1)

[Enrico Schumann]

On Fri, 22 Aug 2014, alexios ghalanos <alexios at 4dscape.com> writes:

> 1. DEoptim is a nonlinear global optimization solver. Global
> optimization is usually reserved for hard to solve non-convex
> problems with many local minima. There is no guarantee of
> optimality not even for convex problems, nor any idea of
> whether the answer you are getting is anything other than a
> local optimum.

There is no *mathematical* guarantee.  But that does not imply
that you cannot use Differential Evolution (the method that
DEoptim implements) with confidence.  Just because you cannot
prove something does not mean that it is not the case.

You do not need mathematical proofs to make meaningful statements
about whether or how well an optimisation method works.[*] For a
given model class (such as particular portfolio-selection
models), you can run experiments.  Experimental results are no
general proof, of course; but they are evidence of how a method
performs for that particular type of model, and typically that is
all that we care about when we apply a method.  In other words,
you may not be able to mathematically prove that a method works,
but you can have empirical evidence that is does.

In practical optimisation, it is not useful to think of "the
[optimal] solution" to a model, and "all the rest".  An
appropriate way to think of it is "no solution, some solution, a
better solution, an even better solution, ..."  and so on.  That
is, think of "iterative improvement", not of optimisation.


[*] If you need an example other than Differential Evolution for
    that, then look at Nelder--Mead.  You cannot prove anything,
    and yet the method "just works".

-- 
Enrico Schumann
Lucerne, Switzerland
http://enricoschumann.net