  We investigate the issue of optimization stability in variance-based
state-specific variational Monte Carlo, discussing the roles of the objective
function, the complexity of wave function ansatz, the amount of sampling
effort, and the choice of minimization algorithm. Using a small cyanine dye
molecule as a test case, we systematically perform minimizations using variants
of the linear method as both a standalone algorithm and in a hybrid combination
with accelerated descent. We demonstrate that adaptive step control is crucial
for maintaining the linear method's stability when optimizing complicated wave
functions and that the hybrid method enjoys both greater stability and
minimization performance. As a verification of variance minimization's
practical utility, we report an excitation energy in the cyanine dye that is in
good agreement with both benchmark quantum chemistry values and results
obtained from state-averaged energy-based variational Monte Carlo.
