On the Geometry and Linear Convergence of Primal-Dual Dynamics

Autor:	Bansode, P., Chinde, V., Wagh, S. R., Pasumarthy, R., Singh, N. M.
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: arXiv admin note: text overlap with arXiv:1905.04521
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.02738 Zobrazit plný text záznamu View this record from Arxiv