A new trust region technique for the maximum weight clique problem Original Research Article

A new simple generalization of the Motzkin–Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin–Straus optimum coincides with such a point. The developed method has complexity image, where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.