A note on upper Lipschitz stability, error bounds, and critical multipliers for Lipschitz-continuous KKT systems

• 成果类型: Article
• 署名作者: Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V.
• 署名单位: Lomonosov Moscow State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0586-z
• 发表日期: 2013
• 页码: 591-604
• 关键词: augmented lagrangian-methods; generalized equations; optimization problems; attraction; BEHAVIOR

摘要

We prove a new local upper Lipschitz stability result and the associated local error bound for solutions of parametric Karush-Kuhn-Tucker systems corresponding to variational problems with Lipschitzian base mappings and constraints possessing Lipschitzian derivatives, and without any constraint qualifications. This property is equivalent to the appropriately extended to this nonsmooth setting notion of noncriticality of the Lagrange multiplier associated to the primal solution, which is weaker than second-order sufficiency. All this extends several results previously known only for optimization problems with twice differentiable data, or assuming some constraint qualifications. In addition, our results are obtained in the more general variational setting.