Generating extreme copositive matrices near matrices obtained from COP-irreducible graphs (Q6536723)

As a main goal of the paper under review is to present an algorithmic procedure for obtaining new families of extremal copositive matrices.\N\NWe recall that a real symmetric \(n\times n\) matrix \(A\) is called copositive if \(\langle Ax,x\rangle\geq 0\) for all \(n\)-tuples of non-negative coordinates. These matrices are completely different from positive semidefinite matrices, and are harder to generate.\NAn important application of copositive matrices can be seen in optimization. However, dealing with these matrices is not as easy as expected.\N\NA copositive matrix is called an extreme point (or extreme element) for the copositive cone (consisting of all copositive matrices of a certain size) is a copositive matrix that cannot lie on the line segment joining any two different copositive matrices.\N\NExtremal copositive matrices have their own applications. In fact, optimization problems revolve about extremal points generally.\NThis is where this paper excels in, where a systematic approach is presented to construct extremal copositive matrices.\NThe obtained results are of significant importance in this field of research, and much further applications of them is expected to be seen in future work by interested researchers.