  We study analytically an intermittent search process in one dimension. There
is an immobile target at the origin and a searcher undergoes a discrete time
jump process starting at $x_0\geq0$, where successive jumps are drawn
independently from an arbitrary jump distribution $f(\eta)$. In addition, with
a probability $0\leq r \leq1$ the position of the searcher is reset to its
initial position $x_0$. The efficiency of the search strategy is characterized
by the mean time to find the target, i.e., the mean first passage time (MFPT)
to the origin. For arbitrary jump distribution $f(\eta)$, initial position
$x_0$ and resetting probability $r$, we compute analytically the MFPT. For the
heavy-tailed L\'evy stable jump distribution characterized by the L\'evy index
$0<\mu < 2$, we show that, for any given $x_0$, the MFPT has a global minimum
in the $(\mu,r)$ plane at $(\mu^*(x_0),r^*(x_0))$. We find a remarkable
first-order phase transition as $x_0$ crosses a critical value $x_0^*$ at which
the optimal parameters change discontinuously. Our analytical results are in
good agreement with numerical simulations.
