TY - JOUR
T1 - Two classes of merit functions for the second-order cone complementarity problem
AU - Chen, Jein Shan
PY - 2006/12
Y1 - 2006/12
N2 - Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.
AB - Recently Tseng (Math Program 83:159-185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.
KW - Error bound
KW - Jordan product
KW - Level set
KW - Merit function
KW - Second-order cone
KW - Spectral factorization
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U2 - 10.1007/s00186-006-0098-9
DO - 10.1007/s00186-006-0098-9
M3 - Article
AN - SCOPUS:33750059427
SN - 1432-2994
VL - 64
SP - 495
EP - 519
JO - Mathematical Methods of Operations Research
JF - Mathematical Methods of Operations Research
IS - 3
ER -