Related papers: Tensor Train accelerated solvers for nonsmooth rig…

In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the…

This study proposes an efficient Newton-type method for the optimal control of switched systems under a given mode sequence. A mesh-refinement-based approach is utilized to discretize continuous-time optimal control problems (OCPs) and…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…

Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…

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.…

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…

Solving partial differential equations of highly featured problems represents a formidable challenge, where reaching high precision across multiple length scales can require a prohibitive amount of computer memory or computing time.…

Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…

Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases.…

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…