  Being motivated by the recent prediction of high-$Q$ supercavity modes in
subwavelength dielectric resonators, we study the second-harmonic generation
from isolated subwavelength AlGaAs nanoantennas pumped by a structured light.
We reveal that nonlinear effects at the nanoscale can be enhanced dramatically
provided the resonator parameters are tuned to the regime of the bound state in
the continuum. We predict a record-high conversion efficiency for nanoscale
resonators that exceeds by two orders of magnitude the conversion efficiency
observed at the conditions of magnetic dipole Mie resonance, thus opening the
way for highly-efficient nonlinear metadevices.
