Related papers: A New Operator Splitting Method for Euler's Elasti…
Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…
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…
We consider the problem of minimizing the sum of three functions, one of which is nonconvex but differentiable, and the other two are convex but possibly nondifferentiable. We investigate the Three Operator Splitting method (TOS) of Davis &…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…
In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use linearized optimal transport theory to prove that the measure-valued…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…
In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry.…
The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…