Related papers: Primal-dual path-following methods and the trust-r…

In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…

Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach,…

\textbf{RE}trieval-\textbf{A}ugmented \textbf{L}LM-based \textbf{M}achine \textbf{T}ranslation (REAL-MT) shows promise for knowledge-intensive tasks like idiomatic translation, but its reliability under noisy retrieval contexts remains…

Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to…

Learning with Noisy Labels (LNL) has attracted significant attention from the research community. Many recent LNL methods rely on the assumption that clean samples tend to have "small loss". However, this assumption always fails to…

Greedy point insertion algorithms have emerged as an attractive tool for the solution of minimization problems over the space of Radon measures. Conceptually, these methods can be split into two phases: first, the computation of a new…

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they…

This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…

In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…

To train robust deep neural networks (DNNs), we systematically study several target modification approaches, which include output regularisation, self and non-self label correction (LC). Two key issues are discovered: (1) Self LC is the…

Deep neural networks need large amounts of labeled data to achieve good performance. In real-world applications, labels are usually collected from non-experts such as crowdsourcing to save cost and thus are noisy. In the past few years,…

With the increasing capabilities of large language models (LLMs), these high-performance models have achieved state-of-the-art results on a wide range of natural language processing (NLP) tasks. However, the models' performance on…

We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…

Computing approximate Karush--Kuhn--Tucker (KKT) points for constrained nonconvex programs is a fundamental problem in mathematical programming. Interior-point trust-region (IPTR) methods are particularly attractive for such problems…

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

The l1-regularized logistic regression is a widely used statistical model in data classification. This paper proposes a dual Newton method based proximal point algorithm (PPDNA) to solve the l1-regularized logistic regression problem with…

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…

Registration networks have shown great application potentials in medical image analysis. However, supervised training methods have a great demand for large and high-quality labeled datasets, which is time-consuming and sometimes impractical…