Exact formulas for the proximal/regular/limiting normal cone of the second-order cone complementarity set

• 成果类型: Article
• 署名作者: Ye, Jane J.; Zhou, Jinchuan
• 署名单位: University of Victoria; Shandong University of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1027-1
• 发表日期: 2017
• 页码: 33-50
• 关键词: optimality conditions; optimization problems; full stability; constraints; PROGRAMS

摘要

The proximal, regular and limiting normal cones to the second-order cone complementarity set play important roles in studying mathematical programs with second-order cone complementarity constraints, second-order cone programs, and the second-order cone complementarity problems. It is needed in the first-order optimality conditions for mathematical programs with second-order cone complementarity constraint, the second-order subdifferential criteria in characterizing the full stability for second-order cone programs and second-order cone complementarity problems, as well as in the characterizing the pseudo-Lipschitz continuity of the solution mapping to parametric second-order cone complementarity problems. In this paper we establish explicit formulas for the proximal, regular, and limiting normal cone of the second-order cone complementarity set.