Improved local convergence results for augmented Lagrangian methods in C2-cone reducible constrained optimization

• 成果类型: Article
• 署名作者: Kanzow, Christian; Steck, Daniel
• 署名单位: University of Wurzburg
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1261-9
• 发表日期: 2019
• 页码: 425-438
• 关键词: upper lipschitz property; inequalities; multipliers; uniqueness

摘要

This paper deals with a class of cone-reducible constrained optimization problems which encompasses nonlinear programming, semidefinite programming, second-order cone programming, and any combination thereof. Using the second-order sufficient condition and a strict version of the Robinson constraint qualification, we provide a (semi-)local error bound which generalizes known results from the literature. Moreover, under the same assumptions, we prove that an augmented Lagrangian method is locally convergent with rate proportional to 1/rho k, where rho k is the penalty parameter, and that {rho k} remains bounded.