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Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The…

Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…

A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time dependent transport equation. Using these solutions we use the dynamic mode decomposition (DMD) to form an approximate…

Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in…

With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…

Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…

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…

In this study, we explore the use of Convolutional Neural Networks for improving train speed estimation accuracy, addressing the complex challenges of modern railway systems. We investigate three CNN architectures - single-branch 2D,…

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…

Convolutional Neural Networks(CNNs) has achieved remarkable performance breakthrough in Euclidean structure data. Recently, aggregation-transformation based Graph Neural networks(GNNs) gradually produce a powerful performance on…

We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes…

Data-efficient image classification is a challenging task that aims to solve image classification using small training data. Neural network-based deep learning methods are effective for image classification, but they typically require…

In this paper, we consider a class of possibly nonconvex, nonsmooth and non-Lipschitz optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing. To solve this class of…

We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

We demonstrate how neural networks can drive mathematical discovery through a case study of the Hadwiger-Nelson problem, a long-standing open problem at the intersection of discrete geometry and extremal combinatorics that is concerned with…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

The deep Convolutional Neural Network (CNN) is the state-of-the-art solution for large-scale visual recognition. Following basic principles such as increasing the depth and constructing highway connections, researchers have manually…

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

Convolutional neural networks (CNNs) have constantly achieved better performance over years by introducing more complex topology, and enlarging the capacity towards deeper and wider CNNs. This makes the manual design of CNNs extremely…