  Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetized
plasmas. In the context of magnetic confinement fusion devices, this leads to
an enhanced transport of particles, momentum, and energy, thereby degrading
confinement. In this work, we elaborate on the application of the adjoint
method to efficiently determine the variation of linear growth rates for plasma
microstabilities concerning a general set of external parameters within the
local $\delta \! f$-gyrokinetic model. We then offer numerical verification of
this approach. When coupled with gradient-based techniques, this methodology
can facilitate the optimization process for the microstability of the confined
plasmas across a high-dimensional parameter space. We present a numerical
demonstration wherein the ion-temperature gradient (ITG) instability growth
rate in a tokamak plasma is minimized with respect to flux surface shaping
parameters. The adjoint method approach demonstrates a significant
computational speed-up compared to a finite-difference gradient calculation.
