A General Regularized Continuous Formulation for the Maximum Clique Problem

In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin–Straus formulation, and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a global and a local sense. We further analyze, from a computational point of view, two different regularizers that satisfy the general conditions.