  Convex optimization challenges are currently pervasive in many science and
engineering domains. In many applications of convex optimization, such as those
involving multi-agent systems and resource allocation, the objective function
can persistently switch during the execution of an optimization algorithm.
Motivated by such applications, we analyze the effect of persistently switching
objectives in continuous-time optimization algorithms. In particular, we take
advantage of existing robust stability results for switched systems with
distinct equilibria and extend these results to systems described by
differential inclusions, making the results applicable to recent optimization
algorithms that employ differential inclusions for improving efficiency and/or
robustness. Within the framework of hybrid systems theory, we provide an
accurate characterization, in terms of Omega-limit sets, of the set to which
the optimization dynamics converge. Finally, by considering the switching
signal to be constrained in its average dwell time, we establish semi-global
practical asymptotic stability of these sets with respect to the dwell-time
parameter.
