Asymptotic convergence of constrained primal-dual dynamics

作者：Cherukuri Ashish^*; Mallada Enrique; Cortes Jorge

来源：Systems & Control Letters, 2016, 87: 10-15.

DOI：10.1016/j.sysconle.2015.10.006

• Primal-dual dynamics
• Constrained optimization
• Saddle points
• Discontinuous dynamics
• Caratheodory solutions

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.

• 出版日期2016-1