We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
Newton method; (stabilized) sequential quadratic programming; constrained optimization; variational problem; second-order sufficiency; (non)critical Lagrange multipliers
