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This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting…
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter…
Model-based reinforcement learning (MBRL) with autoregressive world models suffers from compounding errors, whereas diffusion world models mitigate this by generating trajectory segments jointly. However, existing diffusion guides are…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…
Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…
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.…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
Model order reduction (MOR) techniques have always struggled in compressing information for advection dominated problems. Their linear nature does not allow to accelerate the slow decay of the Kolmogorov $N$--width of these problems. In the…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
Centered finite-difference discretizations of convection--diffusion equations may oscillate when convection dominates at the mesh scale. For homogeneous Dirichlet problems with constant coefficients on uniform Cartesian grids, we derive…
The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain $\Omega$. Firstly, we construct a…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…
In the context of continuously rising global air traffic, efficient and safe Conflict Detection and Resolution (CD&R) is paramount for air traffic management. Although Deep Reinforcement Learning (DRL) offers a promising pathway for CD&R…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Approximating model predictive control (MPC) using imitation learning (IL) allows for fast control without solving expensive optimization problems online. However, methods that use neural networks in a simple L2-regression setup fail to…