On the multiplier-penalty-approach for quasi-variational inequalities

• 成果类型: Article
• 署名作者: Kanzow, Christian
• 署名单位: University of Wurzburg
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0973-3
• 发表日期: 2016
• 页码: 33-63
• 关键词: augmented lagrangian-methods; linear-dependence condition; gap function; optimization; CONVERGENCE; formulation; constraints

摘要

The multiplier-penalty approach is one of the classical methods for the solution of constrained optimization problems. This method was generalized to the solution of quasi-variational inequalities by Pang and Fukushima (Comput Manag Sci 2:21-56, 2005). Based on the recent improvements achieved for the multiplier-penalty approach for optimization, we generalize the method by Pang and Fukushima for quasi-variational inequalities in several respects: (a) We allow to compute inexact KKT-points of the resulting subproblems; (b) We improve the existing convergence theory; (c) We investigate some special classes of quasi-variational inequalities where the resulting subproblems turn out to be easy to solve. Some numerical results indicate that the corresponding method works quite reliable in practice.