IMPLICIT AUGMENTED LAGRANGIAN AND GENERALIZED OPTIMIZATION.

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented Lagrangian framework to this broad problem class, pre-serving an implicit formulation and introducing auxiliary variables merely as a formal device. This, however, gives rise to a generalized augmented Lagrangian function that lacks regularity. Based on parametric optimization, we develop a tailored stationarity concept to better qualify the iterates, generated as approximate solutions to a sequence of subproblems. Using this variational characterization and the lifted representation, asymptotic properties and convergence guarantees are established for a safeguarded augmented Lagrangian scheme. Numerical examples showcase the modelling versatility gained by dropping convexity assumptions and the practical benefits of the advocated implicit approach. [ABSTRACT FROM AUTHOR]