This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually vi...

In this paper, we apply our proposed computing algorithm for numerical solution of semiconductor device energy balance equation in carrier temperature simulation. This robust simulation based on finite volume discertization scheme and monotone iterative algorithm is successfully developed and implemented for intrinsic investigation of submicron MOSFET device. Simulation results demonstrate MOSF...

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

We present an infeasible-interior-point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence. By choosing the value of a parameter in appropriate ways, polynomial complexity and convergence with Q-order up to (but not including...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

The core is a set–valued solution concept for cooperative games. In situations where the characteristic function is not monotone the classical definition may not be sufficient. Hence, we propose a subset of the core that is called subcoalition–perfect core. It will be proven that the subcoalition–perfect core coincides with the set of non–negative core allocations. Furthermore, a general mathem...

Since monotone methods have been initiated by Kamke 1 and Müler 2 , and developed further by Krasnoselskii 3, 4 , Matano 5 , and Smith 6 , the theory and application of monotone dynamics have become increasingly important see 7–18 . It is well known that the quasimonotone condition is very important in studying the asymptotic behaviors of dynamical systems. If this condition is satisfied, the s...

It is well known that gap functions play a major role in developing error bounds for strongly monotone and affine monotone variational inequalities. However the error bound would be important from the point of view of computation if the gap function values diminishes on sequence of points which converge to a solution of the variational inequality. A gap function exhibiting such behavior is term...