  This paper introduces a novel distributed optimization technique for
networked systems, which removes the dependency on specific parameter choices,
notably the learning rate. Traditional parameter selection strategies in
distributed optimization often lead to conservative performance, characterized
by slow convergence or even divergence if parameters are not properly chosen.
In this work, we propose a systems theory tool based on the port-Hamiltonian
formalism to design algorithms for consensus optimization programs. Moreover,
we propose the Mixed Implicit Discretization (MID), which transforms the
continuous-time port-Hamiltonian system into a discrete time one, maintaining
the same convergence properties regardless of the step size parameter. The
consensus optimization algorithm enhances the convergence speed without
worrying about the relationship between parameters and stability. Numerical
experiments demonstrate the method's superior performance in convergence speed,
outperforming other methods, especially in scenarios where conventional methods
fail due to step size parameter limitations.
