Growth behavior of two classes of merit functions for symmetric cone complementarity problems

S. H. Pan, J. S. Chen*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

6 引文 斯高帕斯(Scopus)

摘要

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth implicit Lagrangian complementarity function, respectively. We show that, for the linear symmetric cone complementarity problem (SCLCP), both the EP merit functions and the implicit Lagrangian merit function are coercive if the underlying linear transformation has the P-property; for the general SCCP, the EP merit functions are coercive only if the underlying mapping has the uniform Jordan P-property, whereas the coerciveness of the implicit Lagrangian merit function requires an additional condition for the mapping, for example, the Lipschitz continuity or the assumption as in (45).

原文英語
頁(從 - 到)167-191
頁數25
期刊Journal of Optimization Theory and Applications
141
發行號1
DOIs
出版狀態已發佈 - 2009 四月

ASJC Scopus subject areas

  • 控制和優化
  • 管理科學與經營研究
  • 應用數學

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