@article{d2a29e0937404845a151fd1c5d58fa7a,
title = "A merit function method for infinite-dimensional SOCCPs",
abstract = "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(r{\'e}chet)-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.",
keywords = "Complementarity, Hilbert space, Merit functions, Second-order cone",
author = "Yungyen Chiang and Shaohua Pan and Chen, {Jein Shan}",
note = "Funding Information: E-mail addresses: chiangyy@math.nsysu.edu.tw (Y. Chiang), shhpan@scut.edu.cn (S. Pan), jschen@math.ntnu.edu.tw (J.-S. Chen). 1 The author{\textquoteright}s work is partially supported by grants from the National Science Council of the Republic of China. 2 The author{\textquoteright}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{\textquoteright}s work is partially supported by National Science Council of Taiwan.",
year = "2011",
month = nov,
day = "1",
doi = "10.1016/j.jmaa.2011.05.019",
language = "English",
volume = "383",
pages = "159--178",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",
}