On the natural merit function for solving complementarity problems

• 成果类型: Article
• 署名作者: Andreani, R.; Judice, J. J.; Martinez, J. M.; Patricio, J.
• 署名单位: Instituto Politecnico de Tomar; Universidade Estadual de Campinas; Universidade de Coimbra; Instituto de Telecomunicacoes; Institute of Telecommunications - Coimbra; Universidade de Coimbra
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0336-z
• 发表日期: 2011
• 页码: 211-223
• 关键词: projected gradient methods; nonlinear complementarity; variational-inequalities; smooth optimization; REFORMULATION; algorithms

摘要

Complementarity problems may be formulated as nonlinear systems of equations with non-negativity constraints. The natural merit function is the sum of squares of the components of the system. Sufficient conditions are established which guarantee that stationary points are solutions of the complementarity problem. Algorithmic consequences are discussed.