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We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…
Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
In this paper we develop a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
We introduce and investigate the asymptotic behaviour of the trajectories of a second order dynamical system with Tikhonov regularization for solving a monotone equation with single valued, monotone and continuous operator acting on a real…
In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…
There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…
Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved micro-structural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based…