Passivity-Based Generalization of Primal-Dual Dynamics for Non-Strictly Convex Cost Functions

Abstract: In this paper, we revisit primal-dual dynamics for convex optimization and present a generalization of the dynamics based on the concept of passivity. It is then proved that supplying a stable zero to one of the integrators in the dynamics allows one to eliminate the assumption of strict convexity on the cost function based on the passivity paradigm together with the invariance principle for Caratheodory systems. We then show that the present algorithm is also a generalization of existing augmented Lagrangian-based primal-dual dynamics, and discuss the benefit of the present generalization in terms of noise reduction and convergence speed.