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In this paper we introduce disropt, a Python package for distributed optimization over networks. We focus on cooperative set-ups in which an optimization problem must be solved by peer-to-peer processors (without central coordinators) that have access only to partial knowledge of the entire problem. To reflect this, agents in disropt are modeled as entities that are initialized with their local knowledge of the problem. Agents then run local routines and communicate with each other to solve the global optimization problem. A simple syntax has been designed to allow for an easy modeling of the problems. The package comes with many distributed optimization algorithms that are already embedded. Moreover, the package provides full-fledged functionalities for communication and local computation, which can be used to design and implement new algorithms. disropt is available at github.com/disropt/disropt under the GPL license, with a complete documentation and many examples.

In this paper we propose a new control-oriented design technique to enhance the algorithmic performance of the distributed gradient tracking algorithm. We focus on a scenario in which agents in a network aim to cooperatively minimize the sum of convex, quadratic cost functions depending on a common decision variable. By leveraging a recent system-theoretical reinterpretation of the considered algorithmic framework as a closed-loop linear dynamical system, the proposed approach generalizes the diagonal gain structure associated to the existing gradient tracking algorithms. Specifically, we look for closed-loop gain matrices that satisfy the sparsity constraints imposed by the network topology, without however being necessarily diagonal, as in existing gradient tracking schemes. We propose a novel procedure to compute stabilizing sparse gain matrices by solving a set of nonlinear matrix inequalities, based on the solution of a sequence of approximate linear versions of such inequalities. Numerical simulations are presented showing the enhanced performance of the proposed design compared to existing gradient tracking algorithms.