  We introduce a new form of Lagrangian and propose a simple first-order
algorithm for nonconvex optimization with nonlinear equality constraints. We
show the algorithm generates bounded dual iterates, and establish the
convergence to KKT points under standard assumptions. The key features of the
method are: (i) it does not require boundedness assumptions on the iterates and
the set of multipliers; (ii) it is a single-loop algorithm that does not
involve any penalty subproblems.
