General interior-point maps and existence of weighted paths for nonlinear semidefinite complementarity problems

• 成果类型: Article
• 署名作者: Monteiro, RDC; Zanjácomo, PR
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.25.3.381.12216
• 发表日期: 2000
• 页码: 381-399
• 关键词: primal-dual algorithms; polynomial convergence; DIRECTIONS; FAMILY

摘要

Extending the previous work of Monteiro and Pang (1998), this paper studies properties of fundamental maps that can be used to describe the central path of the monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. Instead of focusing our attention on a specific map as was done in the approach of Monteiro and Pang (1998), this paper considers a general form of a fundamental map and introduces conditions on the map that allow us to extend the main results of Monteiro and Pang (1998) to this general map. Each fundamental map leads to a family of weighted continuous trajectories which include the central trajectory as a special case. Hence, for complementarity problems over the cone of symmetric positive semidefinite matrices, the notion of weighted central path depends on the fundamental map used to represent the central path.