Passivity-Based Generalization of Primal-Dual Dynamics for Non-Strictly Convex Cost Functions
For researchers in convex optimization and control, this provides a theoretical generalization that relaxes a key assumption, though the practical impact is incremental.
The paper generalizes primal-dual dynamics for convex optimization by using passivity to eliminate the need for strict convexity of the cost function, and shows benefits in noise reduction and convergence speed.
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.