IfK is a closed convex cone and if L is a linear operator having L (K) ⊆ K, then L is a positive operator on K and L preserves inequality with respect to K. The set of all positive operators on K is denoted by π (K). If K∗ is the dual of K, then its complementarity set is C (K) := {(x, s) ∈ K ×K | 〈x, s〉 = 0} . Such a set arises as optimality conditions in convex optimization, and a linear oper...

The reachability problem for timed automata asks if there exists a path from an initial state to a target state. The standard solution to this problem involves computing the zone graph of the automaton, which in principle could be infinite. In order to make the graph finite, zones are approximated using an extrapolation operator. For reasons of efficiency in current algorithms extrapolation of ...

An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.

We are concerned with the study of a class of forward-backward penalty schemes for solving variational inequalities 0 ∈ Ax+NC(x) where H is a real Hilbert space, A : H ⇉ H is a maximal monotone operator, and NC is the outward normal cone to a closed convex set C ⊂ H. Let Ψ : H → R be a convex differentiable function whose gradient is Lipschitz continuous, and which acts as a penalization functi...

The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...

The Chvátal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It was recently shown that the Chvátal-Gomory closure of a strictly convex body is also a rational polytope. In this note, we show that the split closure of a strictly convex body is defined by a finite number of split disjunctions, but is not necessarily polyhedral. We also give a closed form expr...

In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

1 Domains with Convex Closure Saks and Yu (2005) proved that if D is convex then every monotone deterministic allocation rule is implementable. We prove in this appendix the following generalization of their result: Theorem 1 Every domain with a convex closure is a proper monotonicity domain.