  Simultaneous perturbation stochastic approximation (SPSA) is widely used in
stochastic optimization due to its high efficiency, asymptotic stability, and
reduced number of required loss function measurements. However, the standard
SPSA algorithm needs to be modified to deal with constrained problems. In
recent years, sequential quadratic programming (SQP)-based projection ideas and
penalty ideas have been analyzed. Both ideas have convergence results and a
potentially wide range of applications, but with some limitations in practical
consideration, such as computation time, complexity, and feasibility guarantee.
We propose an SPSA-based switch updating algorithm, which updates based on the
loss function or the inequality constraints, depending on current feasibility
in each iteration. We show convergence results for the algorithm, and analyze
its properties relative to other methods. We also numerically compare the
switch updating algorithm with the penalty function approach for two
constrained examples.
