  Posynomials are nonnegative combinations of monomials with possibly
fractional and both positive and negative exponents. Posynomial models are
widely used in various engineering design endeavors, such as circuits,
aerospace and structural design, mainly due to the fact that design problems
cast in terms of posynomial objectives and constraints can be solved
efficiently by means of a convex optimization technique known as geometric
programming (GP). However, while quite a vast literature exists on GP-based
design, very few contributions can yet be found on the problem of identifying
posynomial models from experimental data. Posynomial identification amounts to
determining not only the coefficients of the combination, but also the
exponents in the monomials, which renders the identification problem
numerically hard. In this draft, we propose an approach to the identification
of multivariate posynomial models, based on the expansion on a given
large-scale basis of monomials. The model is then identified by seeking
coefficients of the combination that minimize a mixed objective, composed by a
term representing the fitting error and a term inducing sparsity in the
representation, which results in a problem formulation of the ``square-root
LASSO'' type, with nonnegativity constraints on the variables. We propose to
solve the problem via a sequential coordinate-descent scheme, which is suitable
for large-scale implementations.
