We study the computational complexity of finding extremal principal minors of a positive definite matrix. In particular, we focus on the NP-hard problem of maximizing the determinant over the set of principal submatrices of a given order. This problem arises in the area of statistical design,...

The boolean quadric polytope Pn is the convex hull in d:= (n;l) dimensions of the binary solutions of XiXj = Yij, for all i j in N := {l, 2, ... , n} (n ~ 2). The polytope is naturally modeled by a somewhat larger polytope; namely, Qn the solution set of Yij :5 Xi, Yij :5 Xj, X, + Xj :5 1 + Yij,...