Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Framework of Constraint Preserving Update Schemes for Optimization on
  Stiefel Manifold   This paper considers optimization problems on the Stiefel manifold
$X^{\mathsf{T}}X=I_p$, where $X\in \mathbb{R}^{n \times p}$ is the variable and
$I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving
update schemes is proposed by decomposing each feasible point into the range
space of $X$ and the null space of $X^{\mathsf{T}}$. While this general
framework can unify many existing schemes, a new update scheme with low
complexity cost is also discovered. Then we study a feasible
Barzilai-Borwein-like method under the new update scheme. The global
convergence of the method is established with an adaptive nonmonotone line
search. The numerical tests on the nearest low-rank correlation matrix problem,
the Kohn-Sham total energy minimization and a specific problem from statistics
demonstrate the efficiency of the new method. In particular, the new method
performs remarkably well for the nearest low-rank correlation matrix problem in
terms of speed and solution quality and is considerably competitive with the
widely used SCF iteration for the Kohn-Sham total energy minimization.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg