  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.
