A New Lagrangian-Based First-Order Method for Nonconvex Constrained Optimization

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.