Copositivity detection by difference-of-convex decomposition and \(\omega \)-subdivision
The paper introduces difference-of-convex based approaches to copositivity testing. The authors propose an algorithm to detect copositivity of a given symmetric matrix which combines linear programming and convex quadratic programming technology with spectral information. Three copositivity tests are presented. The algorithm either provides a guarantee for copositivity, or delivers a violating vector as a certificate for non-copositivity. For the branch and bound algorithm, the choice of spectral difference-of-convex decomposition and a robustification step are discussed. Some empirical tests results are presented on randomly generated matrices, and checking copositivity on the maximum clique problem.
spectral difference-of-convex decomposition
scientific article; zbMATH DE number 6160889
scientific article