A quasi-Newton strategy for the sSQP method for variational inequality and optimization problems

• 成果类型: Article
• 署名作者: Fernandez, Damian
• 署名单位: National University of Cordoba
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0493-8
• 发表日期: 2013
• 页码: 199-223
• 关键词: local convergence; algorithm; sqp

摘要

The quasi-Newton strategy presented in this paper preserves one of the most important features of the stabilized Sequential Quadratic Programming method, the local convergence without constraint qualifications assumptions. It is known that the primal-dual sequence converges quadratically assuming only the second-order sufficient condition. In this work, we show that if the matrices are updated by performing a minimization of a Bregman distance (which includes the classic updates), the quasi-Newton version of the method converges superlinearly without introducing further assumptions. Also, we show that even for an unbounded Lagrange multipliers set, the generated matrices satisfies a bounded deterioration property and the Dennis-Mor, condition.