A relaxed constant positive linear dependence constraint qualification and applications

• 成果类型: Article
• 署名作者: Andreani, Roberto; Haeser, Gabriel; Laura Schuverdt, Maria; Silva, Paulo J. S.
• 署名单位: Universidade de Sao Paulo; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); National University of La Plata; Universidade Federal de Sao Paulo (UNIFESP); Universidade Estadual de Campinas
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0456-0
• 发表日期: 2012
• 页码: 255-273
• 关键词: augmented lagrangian-methods

摘要

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.