Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Large-Scale Matrix and Tensor Decomposition with Structured
  Factors: A Unified Nonconvex Optimization Perspective   The proposed article aims at offering a comprehensive tutorial for the
computational aspects of structured matrix and tensor factorization. Unlike
existing tutorials that mainly focus on {\it algorithmic procedures} for a
small set of problems, e.g., nonnegativity or sparsity-constrained
factorization, we take a {\it top-down} approach: we start with general
optimization theory (e.g., inexact and accelerated block coordinate descent,
stochastic optimization, and Gauss-Newton methods) that covers a wide range of
factorization problems with diverse constraints and regularization terms of
engineering interest. Then, we go `under the hood' to showcase specific
algorithm design under these introduced principles. We pay a particular
attention to recent algorithmic developments in structured tensor and matrix
factorization (e.g., random sketching and adaptive step size based stochastic
optimization and structure-exploiting second-order algorithms), which are the
state of the art---yet much less touched upon in the literature compared to
{\it block coordinate descent} (BCD)-based methods. We expect that the article
to have an educational values in the field of structured factorization and hope
to stimulate more research in this important and exciting direction.

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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex