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