Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Geometry and Linear Convergence of Primal-Dual Dynamics   The paper proposes a variational-inequality based primal-dual dynamic that
has a globally exponentially stable saddle-point solution when applied to solve
linear inequality constrained optimization problems. A Riemannian geometric
framework is proposed wherein we begin by framing the proposed dynamics in a
fiber-bundle setting endowed with a Riemannian metric that captures the
geometry of the gradient (of the Lagrangian function). A strongly monotone
gradient vector field is obtained by using the natural gradient adaptation on
the Riemannian manifold. The Lyapunov stability analysis proves that this
adaption leads to a globally exponentially stable saddle-point solution.
Further, with numeric simulations we show that the scaling a key parameter in
the Riemannian metric results in an accelerated convergence to the saddle-point
solution.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci