On Oct 19, 2010, at 9:40 AM, MM wrote:
The remaining 3 parameters are number of days in the historical measurements (they can be bound by 500 days)
[...]
Can this then be subdivided as in G. Maxwell's email? Should the optimization be over [1.0, 500.0] in continuous?
I would definitely recommend making [1,500] being a continuous range rather than integers. In your case, it sounds like there is a perfectly sensible interpretation of a fractional value: just interpolate (or fractionally weight) your historical record so that you can compare to a fraction of a day. The point is that optimization over continuous variables is usually much easier than optimizing integer variables, because with continuous variables there you can take small steps "downhill" to improve your objective.
As a first step, I would just use local optimization over all of these variables; now that they are continuous variables (with at least a piecewise differentiable function), that should be a lot easier. Try different local optimization methods and see which one works well.
Then try various techniques to get a more global optimum. e.g. you can use the MLSL algorithm in NLopt to do a sequence of local optimizations to explore the space, or you could use the other global algorithms.
Or you could do global optimization over only a subset of the variables as Gregory suggested, using that as a starting point for local optimization, although in general this does not give the global optimum.
Of course, the difficulty with global optimization of arbitrary nonlinear functions is that in general it can be arbitrarily hard (even NP hard), and one doesn't even usually know whether the global optimum has been reached. In practice, then, you typically have to content yourself with a solution that is "good enough" rather than strictly demanding the global optimum. And you hope that your problem is one without too many local optima so that you can find a reasonably global optimum, if not necessarily *the* global optimum, in a reasonable time.
Steven _______________________________________________ NLopt-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/nlopt-discuss
