On September 21 at 3:00 p.m., a seminar will be held at KTU FMNS. Assoc. Prof. Tatiana Tchemisova (University of Aveiro, Portugal) will give a talk entitled:
“Algorithmic Representation of Minimal Zeros of a Copositive Matrix via Maximal Cliques of a Graph”
The seminar will take place in Room 326, Studentų St. 50, Kaunas.
Abstract of the presentation.There exists a deep and fruitful interplay between copositive matrices and graph theory. On one hand, copositive matrices serve as a powerful framework for modeling and solving complex problems in graph theory. On the other hand, graph-theoretical concepts offer valuable tools for analyzing fundamental properties of copositive matrices, including their spectra and eigenstructures.
In this paper, we explore new dimensions of this relationship by examining the structure of the set of normalized zeros of a copositive matrix. We establish that this set can be described as a union of convex hulls formed from particular subsets of minimal zeros. We further demonstrate that these subsets are closely related to the maximal cliques of a specially constructed graph, which is defined based on the set of minimal zeros of the matrix.
Moreover, we propose an algorithm to systematically compute both the set of normalized minimal zeros and the complete set of normalized zeros of a given copositive matrix.
Registration for this seminar is open until September 18, 12:00 p.m.