[Rd] Numerical optimisation and "non-feasible" regions

From: Mathieu Ribatet <mathieu.ribatet_at_epfl.ch>
Date: Wed, 06 Aug 2008 18:25:45 +0200

Dear list,

I'm currently writing a C code to compute the (composite) likelihood - well this is done but not really robust. The C code is wrapped in an R one which call the optimizer routine - optim or nlm. However, the fitting procedure is far from being robust as the parameter space depends on the parameter - I have a covariance matrix that should be a valid one for example.

Currently, I set in my header file something like #define MINF -1.0e120 and test if we are in a non-feasible region, then setting the log-composite likelihood to MINF. The problem I see with this approach is that for a quite large non-feasible region, we have a kind of plateau where the log-composite likelihood is constant and may have potential issues with the optimizer. The other issue is that the gradient is now badly estimated using finite-differences.

Consequently, I'm not sure this is the most relevant approach as it seems that (especially the BFGS method, probably due to the estimation of the gradient) the optimization is really sensitive to this "strategy" and fails (quite often).

As I'm (really) not an expert in optimization problems, do you know good ways to deal with non-feasible regions? Or do I need to reparametrize my model so that all parameters belong to $\mathbb{R}$ - which should be not so easy...

Thanks for your expertise!

Institute of Mathematics
Ecole Polytechnique Fédérale de Lausanne
CH-1015 Lausanne   Switzerland
Tel: + 41 (0)21 693 7907

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Received on Wed 06 Aug 2008 - 16:51:52 GMT

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