Complex diseases are often characterized by coordinated expression alterations of genes and proteins which are grouped together in a molecular network. Identifying such interconnected and jointly altered gene/protein groups from functional omics data and a given molecular interaction network is a key challenge in bioinformatics. We describe GenePEN, a penalized logistic regression approach for sample classification via convex optimization, using a newly designed Pairwise Elastic Net penalty that favors the selection of discriminative genes/proteins according to their connectedness in a molecular interaction graph. An efficient implementation of the method finds provably optimal solutions on high-dimensional omics data in a few seconds and is freely available at http://lcsb-portal.uni.lu/bioinformatics.