  The DESC stellarator optimization code takes advantage of advanced numerical
methods to search the full parameter space much faster than conventional tools.
Only a single equilibrium solution is needed at each optimization step thanks
to automatic differentiation, which efficiently provides exact derivative
information. A Gauss-Newton trust-region optimization method uses second-order
derivative information to take large steps in parameter space and converges
rapidly. With just-in-time compilation and GPU portability, high-dimensional
stellarator optimization runs take orders of magnitude less computation time
with DESC compared to other approaches. This paper presents the theory of the
DESC fixed-boundary local optimization algorithm along with demonstrations of
how to easily implement it in the code. Example quasi-symmetry optimizations
are shown and compared to results from conventional tools. Three different
forms of quasi-symmetry objectives are available in DESC, and their relative
advantages are discussed in detail. In the examples presented, the triple
product formulation yields the best optimization results in terms of minimized
computation time and particle transport. This paper concludes with an
explanation of how the modular code suite can be extended to accommodate other
types of optimization problems.
