Goyens, FlorentinEftekhari, ArminBoumal, Nicolas2024-05-012024-05-012024-05-012024-04-1110.1007/s10957-024-02421-6https://infoscience.epfl.ch/handle/20.500.14299/207664WOS:001200378500002We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the geometric formalism of Riemannian optimization. Using a smooth exact penalty function known as Fletcher's augmented Lagrangian, we propose an algorithm to minimize the penalized cost function which reaches ε-approximate second-order critical points of the original optimization problem in at most O(ε^-3) iterations. This improves on current best theoretical bounds. Along the way, we show new properties of Fletcher's augmented Lagrangian, which may be of independent interest.TechnologyPhysical SciencesNonconvex OptimizationConstrained OptimizationAugmented LagrangianComplexityRiemannian Optimizationtext::journal::journal article::research article