相关论文: Nonmonotone Globalization for Anderson Acceleratio…

We propose a new framework to design and analyze accelerated methods that solve general monotone equation (ME) problems $F(x)=0$. Traditional approaches include generalized steepest descent methods and inexact Newton-type methods. If $F$ is…

Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess…

We give a complete characterization of the behavior of the Anderson acceleration (with arbitrary nonzero mixing parameters) on linear problems. Let n be the grade of the residual at the starting point with respect to the matrix defining the…

When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation,…

A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…

In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…

Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under…

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly…

This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the…

The topological obstructions on the attitude space of a rigid body make global asymptotic stabilization impossible using continuous state-feedback. This paper presents novel algorithms to overcome such topological limitations and achieve…

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence…

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…

Physics-guided deep learning is an important prevalent research topic in scientific machine learning, which has tremendous potential in various complex applications including science and engineering. In these applications, data is expensive…

This paper proposes an accelerated method for approximately solving partially observable Markov decision process (POMDP) problems offline. Our method carefully combines two existing tools: Anderson acceleration (AA) and the fast informed…

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…

We consider two modifications of the Arrow-Hurwicz (AH) iteration for solving the incompressible steady Navier-Stokes equations for the purpose of accelerating the algorithm: grad-div stabilization, and Anderson acceleration. AH is a…

We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with…

We consider the problem of non-smooth convex optimization with linear equality constraints, where the objective function is only accessible through its proximal operator. This problem arises in many different fields such as statistical…

The alternating direction method of multipliers (ADMM) has been widely adopted in low-rank approximation and low-order model identification tasks; however, the performance of nonconvex ADMM is highly reliant on the choice of penalty…

Predicting the behavior of a magnetically confined fusion plasma over long time periods requires methods that can bridge the difference between transport and turbulent time scales. The nonlinear transport solver, Tango, enables simulations…