  We analyze a one-dimensional intermittent random walk on an unbounded domain
in the presence of stochastic resetting. In this process, the walker alternates
between local intensive search, diffusion, and rapid ballistic relocations in
which it does not react to the target. We demonstrate that Poissonian resetting
leads to the existence of a non-equilibrium steady state. We calculate the
distribution of the first arrival time to a target along with its mean and show
the existence of an optimal reset rate. In particular, we prove that the
initial condition of the walker, i.e., either starting diffusely or relocating,
can significantly affect the long-time properties of the search process.
Moreover, we demonstrate the presence of distinct parameter regimes for the
global optimization of the mean first arrival time when ballistic and diffusive
movements are in direct competition.
