A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classe...

We consider the general class of strongly Fejer monotone map-pings and some of their basic properties. These properties are useful for a convergence theory of corresponding iterative methods which are widely used to solve convex problems (see e.g. 3], 6], 7], 10]). In part I we study the relation between these mappings and their relaxations. 1 Strongly Fejer monotone mappings Let H be a (real) ...

Abstract In a real Hilbert space, let GSVI and CFPP represent general system of variational inequalities common fixed point problem countable family nonexpansive mappings an asymptotically mapping, respectively. this paper, via new subgradient extragradient implicit rule, we introduce analyze two iterative algorithms for solving the monotone bilevel equilibrium (MBEP) with constraints, i.e., st...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas σ1, σ2, and σ3, the composition problem is to find an equivalent mapping over only σ1 and σ3. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many σ2 symbols as possible, even if not all can be eliminated. It c...

Such a set G is said to be maximal monotone if it is maximal among monotone sets in the sense of set inclusion, and a mapping T is said to be maximal monotone if its graph G(T) is a maximal monotone set. For reflexive Banach spaces X and mappings T with D(T)~X, the basic result obtained independently by Browder [2] and Minty [20] states that if T is a monotone operator from D(T)=X to X* which i...

Let H be a real Hilbert space. A mapping A : D(A) ⊆ H → H is said to be monotone if ⟨Ax − Ay, x − y⟩ ≥ 0 for every x, y ∈ D(A). A is called maximal monotone if it is monotone and the R(I + rA) = H, the range of (I + rA), for each r > 0, where I is the identity mapping on H. A is said to satisfy the range condition if cl(D(A)) ⊆ R(I + rA) for each r > 0. For monotone mappings, there are many rel...