Distributed and event-triggered optimization in multi-agent networks

This thesis is concerned with the development of distributed optimization methods with adaptive step-size control and event-triggered communication, where the focus is on convex optimization problems with either nonseparable objective function but separable constraints or separable objective function but couplings in the constraints. Regarding a practice related application of the developed algorithms, it is shown how the convex direct current optimal power flow (DC-OPF) problem can be solved distributedly with event-triggered and local communication in a multi-agent network. Moreover, the combined application with a decomposition technique for linear matrix inequalities is described which enables to distributedly solve a semidefinite dual of the nonconvex alternating current optimal power flow (AC-OPF) problem with (close to) local and eventtriggered communication. Numerical results for these applications confirm the good properties of the developed algorithms and show that event-triggered communication yields a considerable reduction of the information exchange in the optimization process.