  Cluster detection plays a fundamental role in the analysis of data. In this
paper, we focus on the use of s-defective clique models for network-based
cluster detection and propose a nonlinear optimization approach that
efficiently handles those models in practice. In particular, we introduce an
equivalent continuous formulation for the problem under analysis, and we
analyze some tailored variants of the Frank-Wolfe algorithm that enable us to
quickly find maximal s-defective cliques. The good practical behavior of those
algorithmic tools, which is closely connected to their support identification
properties, makes them very appealing in practical applications. The reported
numerical results clearly show the effectiveness of the proposed approach.
