  Using recently developed adjoint methods for computing the shape derivatives
of functions that depend on MHD equilibria (Antonsen et al. 2019; Paul et al.
2020), we present the first example of analytic gradient-based optimization of
fixed-boundary stellarator equilibria. We take advantage of gradient
information to optimize figures of merit of relevance for stellarator design,
including the rotational transform, magnetic well, and quasisymmetry near the
axis. With the application of the adjoint method, we reduce the number of
equilibrium evaluations by the dimension of the optimization space ($\sim
50-500$) in comparison with a finite-difference gradient-based method. We
discuss regularization objectives of relevance for fixed-boundary optimization,
including a novel method that prevents self-intersection of the plasma
boundary. We present several optimized equilibria, including a vacuum field
with very low magnetic shear throughout the volume.
