TY - JOUR
T1 - Constructions of complementarity functions and merit functions for circular cone complementarity problem
AU - Miao, Xin He
AU - Guo, Shengjuan
AU - Qi, Nuo
AU - Chen, Jein Shan
N1 - Funding Information:
Xin-He Miao work is supported by National Young Natural Science Foundation (No. 11101302 and No. 61002027) and National Natural Science Foundation of China (No. 11471241). Jein-Shan Chen work is supported by Ministry of Science and Technology, Taiwan.
Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.
AB - In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.
KW - Circular cone complementarity problem
KW - Complementarity function
KW - Merit function
KW - Strong coerciveness
KW - The level sets
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U2 - 10.1007/s10589-015-9781-1
DO - 10.1007/s10589-015-9781-1
M3 - Article
AN - SCOPUS:84957848035
SN - 0926-6003
VL - 63
SP - 495
EP - 522
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 2
ER -