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Sum-of-squares relaxations for polynomial min–max problems over simple sets
We consider min–max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of...
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Sum of squares generalizations for conic sets
Polynomial nonnegativity constraints can often be handled using the sum of squares condition. This can be efficiently enforced using semidefinite...
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Riemannian preconditioned algorithms for tensor completion via tensor ring decomposition
We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed...
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Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings
A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A ....
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Tensor and Multimodal Data Analysis
In this book chapter, we provide a selective review of recent advances in tensor analysis and tensor modeling in statistics and machine learning. We...
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Internet traffic tensor completion with tensor nuclear norm
The incomplete data is a common phenomenon in traffic network because of the high measurement cost, the failure of data collection systems and...
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Transpose-free quasi-minimal residual method based on tensor format for generalized coupled sylvester tensor equations
This paper presents an extension of the transpose-free quasi-minimal residual (TFQMR) method for solving the generalized coupled Sylvester tensor...
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Develo** LSQR Method for Sylvester Quaternion Tensor Equations
In this paper, we consider solving a least-squares problem to the generalized Sylvester quaternion tensor equation. From the properties of...
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Low Rank Tensor Decompositions and Approximations
There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are...
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The Order-p Tensor Linear Complementarity Problem for Images Deblurring
In this paper, we first study the equivalence between the third order tensor linear complementarity problem under the framework of t-product and the...
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Efficient iterative method for generalized Sylvester quaternion tensor equation
In this study, we employ the biconjugate residual (BCR) algorithm in tensor form to deal with the generalized Sylvester quaternion tensor equation in...
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A random sampling algorithm for fully-connected tensor network decomposition with applications
Fully-connected tensor network (FCTN) decomposition is a generalization of the popular tensor train and tensor ring decompositions and has been...
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Tensor denoising via dual Schatten norms
Denoising is an important preprocessing step that can improve the quality of the data and make it more suitable for further analysis, enhance the...
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Modular Tensor Categories, Subcategories, and Galois Orbits
We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes...
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Fast Nonnegative Tensor Factorizations with Tensor Train Model
AbstractTensor train model is a low-rank approximation for multidimensional data. In this article we demonstrate how it can be succesfully used for...
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Tensor sparse representation via Einstein product
Sparse representation has garnered significant attention across multiple fields, including signal processing, statistics, and machine learning. The...
