Related papers: A Semismooth Newton Method for Tensor Eigenvalue C…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear…
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…
Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
In this paper, we study the nonemptiness, compactness, uniqueness, and finiteness of the solution set of a new type of nonlinear complementarity problem, namely the extended horizontal tensor complementarity problem (EHTCP). We introduce…
Tensor completion aimes at recovering missing data, and it is one of the popular concerns in deep learning and signal processing. Among the higher-order tensor decomposition algorithms, the recently proposed fully-connected tensor network…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…
In the paper, a variant of the \ssstar Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild…
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…
Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the…
Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…
The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a…