Related papers: On alternating-conjugate splitting methods
This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which aim to take advantage of separable structures of the original problem by solving a sequence of lower-dimensional MILPs. The…
James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method is just corresponding to the second-order perturbation theory, and cannot be exploited to treat the…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
In this article, we present an extension of the splitting algorithm proposed in [22] to networks of conservation laws with piecewise linear discontinuous flux functions in the unknown. We start with the discussion of a suitable Riemann…
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by…
We describe a new family of coupling designs, extending the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and other irregular treatment spaces. Our approach is to first…
We consider a model predictive control (MPC) setting, where we use the alternating direction method of multipliers (ADMM) to exploit problem structure. We take advantage of interacting components in the controlled system by decomposing its…
In this paper, we present splitting methods that are based on iterative schemes and applied to plasma simulations. The motivation arose of solving the Coulomb collisions, which are modeled by nonlinear stochastic differential equations. We…
In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The key ingredients of our method are: (i) the original Hamiltonian energy is reformulated…