Related papers: On some properties of set-valued tensor complement…

These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…

The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

We consider the problem of recovering an orthogonally decomposable tensor with a subset of elements distorted by noise with arbitrarily large magnitude. We focus on the particular case where each mode in the decomposition is corrupted by…

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…

In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…

The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

We propose a numerical method to obtain an adequate value for the upper bound on the rank for the tensor completion problem on the variety of third-order tensors of bounded tensor-train rank. The method is inspired by the parametrization of…

In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniformization problem. Hence, it is important to identify…

Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative low-rank tensor, and using duality theory, we propose a novel factorization of…