Sahin, Mehmet FatihEftekhari, ArminAlacaoglu, AhmetLatorre Gomez, Fabian RicardoCevher, Volkan2019-09-172019-09-172019-09-172019https://infoscience.epfl.ch/handle/20.500.14299/161210WOS:000535866905060We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to the Polyak-Lojasiewicz and Mangasarian-Fromowitz conditions. 000278535 520__ $$aIn particular, when a first-order solver is used for the inner iterates, we prove that iALM finds a first-order stationary point with (O) over tilde (1/epsilon(3)) calls to the first-order oracle. If, in addition, the problem is smooth and a second-order solver is used for the inner iterates, iALM finds a second-order stationary point with (O) over tilde (1/epsilon(5)) calls to the second-order oracle. These complexity results match the known theoretical results in the literature.ml-aitext::conference output::conference proceedings::conference paper