{"ID":2870713,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.11531","arxiv_id":"2509.11531","title":"Q-Linear Convergence of the Proximal Augmented Lagrangian Method for Non-Convex Conic Programming","abstract":"This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as constraint non-degeneracy, strict complementarity, second-order sufficiency conditions, or a combination of constraint nondegeneracy with strong second-order sufficiency conditions. In contrast, our work demonstrates a Q-linear convergence rate for an inexact version of PALM in the context of non-convex conic programming, without requiring the uniqueness of the Lagrange multipliers. The analysis relies solely on the second-order sufficiency condition and the calmness property of the multiplier mapping, presenting a more relaxed set of conditions for ensuring convergence.","short_abstract":"This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as constraint non-degeneracy, strict complementarity, second-order sufficiency conditi...","url_abs":"https://arxiv.org/abs/2509.11531","url_pdf":"https://arxiv.org/pdf/2509.11531v1","authors":"[\"Ning Zhang\",\"Yi Zhang\"]","published":"2025-09-15T02:45:16Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}