  Knowing if an optimal solution is local or global has always been a hard
question to answer in more sophisticated situations of optimization problems.
In this work, for finite-time and weak isothermal driving processes, we show
the existence of a global optimal protocol for the entropy production. We prove
that by showing its convexity as a functional in the derivative of the
protocol. This property also proves its monotonicity in such a context, which
leads to the satisfaction of the Second Law of Thermodynamics. In the end, we
exemplify that the analytical technique of the Euler-Lagrange equation applied
to overdamped Brownian motion delivers the global optimal protocol, by
comparing it with the results of the global optimization technique of genetic
programming.
