  We present a new optimization method for the group selection problem in
linear regression. In this problem, predictors are assumed to have a natural
group structure and the goal is to select a small set of groups that best fits
the response. The incorporation of group structure in a predictor matrix is a
key factor in obtaining better estimators and identifying associations between
response and predictors. Such a discrete constrained problem is well-known to
be hard, particularly in high-dimensional settings where the number of
predictors is much larger than the number of observations. We propose to tackle
this problem by framing the underlying discrete binary constrained problem into
an unconstrained continuous optimization problem. The performance of our
proposed approach is compared to state-of-the-art variable selection strategies
on simulated data sets. We illustrate the effectiveness of our approach on a
genetic dataset to identify grouping of markers across chromosomes.
