Solvability of Variational Inequalities on Hilbert Lattices

• 成果类型: Article
• 署名作者: Nishimura, Hiroki; Ok, Efe A.
• 署名单位: New York University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1120.0553
• 发表日期: 2012
• 页码: 608-625
• 关键词: nonlinear complementarity-problems; EQUIVALENCE; monotone; THEOREM

摘要

This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory.