﻿
 doi:

DOI: 10.3724/SP.J.1160.2013.00337

Acta Analysis Functionalis Applicata (应用泛函分析学报) 2013/15:4 PP.337-341

## Level-boundedness of the Penalized NR Function for Symmetric Cone Complementarity Problem

• ZHENG Yunsheng 1   GAO Leifu 1
• 1.College of Science, Liaoning Technical University,Fuxin 123000, China

Abstract：
We establish a penalized natural function for symmetric cone complementarity problems and use a trace inequality on Euclidean Jordan algebras to show the level-boundedness of its merit function under a weak condition.

Key words：symmetric cone complementarity problem,level-boundedness,trace inequality,R01-function

ReleaseDate：2015-04-21 14:22:08

1 Yoshise A. Complementarity problems over symmetric cone:A survey of recent developments in several aspects[M].New York:Springer-Verlag,2012.

2 修乃华,韩继业. 对称锥互补问题[J].数学进展,2007,(1):1-12.

3 Xiu N H,Han J Y. Symmetric cone complementarity problems[J].Advances in Mathematics,2007.1-12.

4 Gowda M S,Sznajder R,Tao J. Some P-properties for linear transformations on Euclidean Jordan algebra[J].Linear Al1gebra and Its Applications,2004.203-232.

5 Kong L C,Xiu N H. A penalized NR function for symmetric cone complementarity problems[J].数学进展,2011.173-179.

6 Kong L C,Xiu N H. A penalized NR function for symmetric cone complementarity problems[J].Advances in Mathematics,2011.173-179.

7 Chen X D,Sun D,Sun J. Complementarity functions and numerical expriments on some smoothing Newton methods for second-order-cone complemantarity problems[J].Computational Optimization and Applications,2003.39-56.

8 Chang Y L,Chen J S. Convexity of symmetric cone trace functions in euclidean jordan algebras[J].Journal of Nonlinear and Convex Analysis,2013,(01):53-61.

9 Han D. On the coerciveness of some merit functions for complementarity problems over symmetric cones[J].Journal of Mathematical Analysis and Applications,2007.727-737.

10 Liu Y J,Zhang L W,Wang Y H. Some properties of a class of merit functions symmetric cone complementarity problems[J].Asia-Pacific Journal of Operational Research,2006,(04):473-495.

11 Kum S H,Lim Y D. Coercivity and strong semismoothness of the penalized fisher-burmeister function for the symmetric cone complementarity problem[J].Journal of Optimization Theory and Applications,2009.337-383.

12 Faraut J. Analysis on symmetric cones[M].Oxford:University Press,1994.

13 Faybusovic L. Euclidean Jordan algebras and Interior-point algorithms[J].POSITIVITY,1997.331-357.

14 TTao J,Gowda M S. Some p-properties for nonlinear transformations on euclidean jordan algebras[J].Mathematics of Operations Research,2005.985-1004.

15 Baes M. Spectral functions on Jordan algebras:Differentiability and convexity properties[R].Tech Report CORE,Louvain,Belgium,2004.