Related papers: Operator splitting for coupled linear port-Hamilto…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…
Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical…
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is only concerned with the input-output mapping but not with…
The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing…
An efficient geometric integrator is proposed for solving the perturbed Kepler motion. This method is stable and accurate over long integration time, which makes it appropriate for treating problems in astrophysics, like solar system…
In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…
We discuss structure-preserving time discretization for nonlinear port-Hamiltonian systems with state-dependent mass matrix. Such systems occur, for instance, in the context of structure-preserving nonlinear model order reduction for…
We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes by Staffans to formulate a~suitable concept for port-Hamiltonian systems, which allows a…
The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…