Related papers: Anderson Acceleration of Proximal Gradient Methods
Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…
Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a novel optimization algorithm by adapting Anderson…
Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…
Two adaptive relaxation strategies are proposed for Anderson acceleration. They are specifically designed for applications in which mappings converge to a fixed point. Their superiority over alternative Anderson acceleration is demonstrated…
Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…
Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local…
We consider the application of the type-I Anderson acceleration to solving general non-smooth fixed-point problems. By interleaving with safe-guarding steps, and employing a Powell-type regularization and a re-start checking for strong…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…
Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…
Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alpha\nabla f(x)$. It…
Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…
In this paper, we consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…
Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled…
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…
Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…