Related papers: A Composite Decomposition Method for Large-Scale G…

In optimizing real-world structures, due to fabrication or budgetary restraints, the design variables may be restricted to a set of standard engineering choices. Such variables, commonly called categorical variables, are discrete and…

In Artificial Intelligence with Coalition Structure Generation (CSG) one refers to those cooperative complex problems that require to find an optimal partition, maximising a social welfare, of a set of entities involved in a system into…

Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications…

In modern day simulations of many-body systems much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CV) or reaction coordinates. A vast array of…

This paper explores the non-convex composition optimization in the form including inner and outer finite-sum functions with a large number of component functions. This problem arises in some important applications such as nonlinear…

The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis, the convergence of the…

For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…

Composite optimization problems, where a smooth loss is combined with a nonsmooth regularizer, are common in machine learning and inverse problems. In this work, we study a proximal extension of NAG-GS, a semi-implicit accelerated method…

This paper proposes and analyzes a class of essentially non-oscillatory central discontinuous Galerkin (CDG) methods for general hyperbolic conservation laws. First, we introduce a novel compact, non-oscillatory stabilization mechanism that…

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant…

In this paper, we propose a new measure to gauge the complexity of image classification problems. Given an annotated image dataset, our method computes a complexity measure called the cumulative spectral gradient (CSG) which strongly…

Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multi-agent…

CSG trees are an intuitive, yet powerful technique for the representation of geometry using a combination of Boolean set-operations and geometric primitives. In general, there exists an infinite number of trees all describing the same 3D…

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…

Effective cross-modal retrieval requires robust alignment of heterogeneous data types. Most existing methods focus on bi-modal retrieval tasks and rely on distributional alignment techniques such as Kullback-Leibler divergence, Maximum Mean…

This study presents a divide-and-conquer (DC) approach based on feature space decomposition for classification. When large-scale datasets are present, typical approaches usually employed truncated kernel methods on the feature space or DC…

Recently, a number of competitive methods have tackled unsupervised representation learning by maximising the mutual information between the representations produced from augmentations. The resulting representations are then invariant to…

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…

We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a master node and multiple worker nodes. Generalized Lagrange Coded Computing…

In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG…