A modified simplex partition algorithm to test copositivity

Abstract A real symmetric matrix is copositive if $$x^\top Ax\ge 0$$ x ⊤ A ≥ 0 for all $$x\ge . As and only it on the standard simplex, algorithms to determine copositivity, such as those in Sponsel et al. (J Glob Optim 52:537–551, 2012) Tanaka Yoshise (Pac J 11:101–120, 2015), are based upon creation of increasingly fine simplicial partitions simplices, testing copositivity each. We present a variant that decomposes simplex $$\bigtriangleup $$ △ , say with n vertices, into _1$$ 1 polyhedron $$\varOmega Ω ; then set at most $$(n-1)$$ ( n - ) simplices. show allowing us remove from further consideration. Numerical results examples arise maximum clique problem significant reduction time needed establish matrices.