Title: 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.