\indent Recent advances in mixed-integer nonlinear optimization and the solution of optimization problems with differential equation constraints have heightened interest in methods that may be warm started from a good estimate of a solution. In this context, we present a regularized sequential quadratic programming (SQP) method based on a primal-dual augmented Lagrangian function. Trial steps are computed from carefully chosen subproblems that utilize relationships between traditional SQP, stabilized SQP, and the augmented Lagrangian. Each subproblem is well defined regardless of the rank of the Jacobian, and (to some extent) we challenge the belief that large penalty parameters should be avoided.