Stationary point conditions for the FB merit function associated with symmetric cones

Authors:
Shaohua Pan;Yu-Lin Chang;Jein-Shan Chen
Affiliations:
School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China;Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
Venue:
Operations Research Letters
Year:
2010

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Abstract

For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the Fischer-Burmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P"0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195-215.