Numerical Invariants through Convex Relaxation and Max-Strategy Iteration

In this article we develop a max-strategy improvement algorithm for computing least fixpoints of operators on R (with R := R ∪ {±∞}) that are point-wise maxima of finitely many monotone and order-concave operators. Computing the uniquely determined least fixpoint of such operators is a problem that occurs frequently in the context of numerical program/systems verification/analysis. As an example for an application we discuss how our algorithm can be applied to compute numerical invariants of programs by abstract interpretation based on quadratic templates.