On variational inequalities over polyhedral sets

• 成果类型: Article
• 署名作者: Ioffe, Alexander D.
• 署名单位: Technion Israel Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1077-4
• 发表日期: 2018
• 页码: 261-278
• 关键词: normal maps; THEOREM

摘要

The results on regularity behavior of solutions to variational inequalities over polyhedral sets proved in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But the available proofs are very complicated and practically do not use techniques of variational analysis. The only exception is the proof by Dontchev and Rockafellar of their critical face regularity criterion. In the paper we offer a different approach completely based on polyhedral geometry and a few basic principles of metric regularity theory. It leads to new proofs, that look simpler and shorter, and in addition gives some clarifying geometrical information.