Related papers: The Block-wise Circumcentered-Reflection Method
In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
The advent of neural and Gaussian-based radiance field methods have achieved great success in the field of novel view synthesis. However, specular reflection remains non-trivial, as the high frequency radiance field is notoriously difficult…
The Douglas--Rachford method is a splitting method frequently employed for finding zeroes of sums of maximally monotone operators. When the operators in question are normal cones operators, the iterated process may be used to solve…
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…
We study the two-set feasibility problem of finding a point in the intersection $X\cap Y$ of closed convex sets in a Hilbert space. We propose a generalized composed alternating relaxed projection algorithm (gCARPA) that blends…
We propose a theoretical framework for the image source method that generalizes to arbitrary reflecting boundaries, e.g. boundaries that are curved or even with certain openings. Furthermore, it can seamlessly incorporate boundary…
The basic optimization problem of road design is quite challenging due to a objective function that is the sum of nonsmooth functions and the presence of set constraints. In this paper, we model and solve this problem by employing the…
One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while…
Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix…
Transformer-based methods have improved hyperspectral image classification (HSIC) by modeling long-range spatial-spectral dependencies; however, their attention mechanisms typically rely on dot-product similarity, which mixes feature…
Diffusion models have been increasingly used as strong generative priors for solving inverse problems such as super-resolution in medical imaging. However, these approaches typically utilize a diffusion prior trained at a single scale,…
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappings is useful in obtaining simple and transparent arguments…
Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates…