Strong KKT conditions and weak sharp solutions in convex-composite optimization

• 成果类型: Article
• 署名作者: Zheng, Xi Yin; Ng, Kung Fu
• 署名单位: Yunnan University; Chinese University of Hong Kong
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0277-6
• 发表日期: 2011
• 页码: 259-279
• 关键词: gauss-newton method; banach-spaces; error-bounds; constraint qualifications; metric regularity; minima; inequalities; CONVERGENCE; optimality

摘要

Using variational analysis techniques, we study convex-composite optimization problems. In connection with such a problem, we introduce several new notions as variances of the classical KKT conditions. These notions are shown to be closely related to the notions of sharp or weak sharp solutions. As applications, we extend some results on metric regularity of inequalities from the convex case to the convex-composite case.