Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemannian optimization on the simplex of positive definite matrices   In this work, we generalize the probability simplex constraint to matrices,
i.e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where
$\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size
$n\times n$ for all $i = \{1,\ldots,K \}$. By assuming positive definiteness of
the matrices, we show that the constraint set arising from the matrix simplex
has the structure of a smooth Riemannian submanifold. We discuss a novel
Riemannian geometry for the matrix simplex manifold and show the derivation of
first- and second-order optimization related ingredients.

14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn