This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions f at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate indefinite case. These ...

Extended Affine (EA) equivalence is the relation between two vectorial Boolean functions $F$ and notation="LaTeX">$G$ such that there exist affine permutations notation="LaTeX">$A$ , notation="LaTeX">$B$ an function notation="LaTeX">$...

We study the existence of pure Nash equilibria in weighted congestion games. Let C denote a set of cost functions. We say that C is consistent if every weighted congestion game with cost functions in C possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of cost functions. Specifically, we prove that a nonempty set C of twice continuously differ...