Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity
We study nonasymptotic convergence of primal-dual methods for a class of nonconvex constrained optimization problems under local multiplier regularity. Both the objective and functional inequality constraints are compositions of convex Lipschitz outer functions with smooth nonlinear mappings. Unlike existing analyses requiring regularity globally or along the entire iterate sequence, we impose multiplier regularity only near the feasible set. Using an auxiliary minimax problem with a compact dual set, we derive Lyapunov estimates that identify nearly feasible iterates under feasible initialization and a sufficiently large penalty, without assuming multiplier boundedness. Local regularity ...
| Authors | Linglingzhi Zhu, Jiajin Li |
|---|---|
| Primary category | math.OC |
| Published | 9 July 2026 |
| Last updated at source | 14 October 2026 |
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