TY - JOUR
T1 - A merit function method for infinite-dimensional SOCCPs
AU - Chiang, Yungyen
AU - Pan, Shaohua
AU - Chen, Jein Shan
N1 - Funding Information:
E-mail addresses: [email protected] (Y. Chiang), [email protected] (S. Pan), [email protected] (J.-S. Chen). 1 The author’s work is partially supported by grants from the National Science Council of the Republic of China. 2 The author’s work is supported by Guangdong Natural Science Foundation (No. 9251802902000001) and the Fundamental Research Funds for the Central Universities (SCUT). 3 Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan.
PY - 2011/11/1
Y1 - 2011/11/1
N2 - We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions φt on H×H with the parameter t∈[0,2). We show that the squared norm of φt with tφ(0,2) is a continuously F(réchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.
AB - We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions φt on H×H with the parameter t∈[0,2). We show that the squared norm of φt with tφ(0,2) is a continuously F(réchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.
KW - Complementarity
KW - Hilbert space
KW - Merit functions
KW - Second-order cone
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U2 - 10.1016/j.jmaa.2011.05.019
DO - 10.1016/j.jmaa.2011.05.019
M3 - Article
AN - SCOPUS:79958766289
SN - 0022-247X
VL - 383
SP - 159
EP - 178
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -