On monotonicity and search strategies in face-based copositivity detection algorithms

Abstract Over the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration KKT points or face-based search. Our research question focuses exploiting mathematical properties relative interior minima standard quadratic program (StQP) monotonicity. We derive theoretical related convexity monotonicity function over faces simplex. illustrate with numerical instances up 28 dimensions use in algorithms. The is what traversal through face graph simplex more appropriate which matrix instance; top down bottom approaches. This depends level where minimum StQP can be found, density so-called graph.