Abstract
Recently, Tseng extended several merit functions for the nonlinear complementarity problem to the semidefinite complementarity problem (SDCP) and investigated various properties of those functions. In this paper, we propose a new merit function for the SDCP based on the squared Fischer-Burmeister function and show that it has some favorable properties. Particularly, we give conditions under which the function provides a global error bound for the SDCP and conditions under which it has bounded level sets. We also present a derivative-free method for solving the SDCP and prove its global convergence under suitable assumptions.
The work of the authors was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, Japan. The work of the first author was also supported by the Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
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Yamashita, N., Fukushima, M. (1998). A New Merit Function and a Descent Method for Semidefinite Complementarity Problems. In: Fukushima, M., Qi, L. (eds) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Applied Optimization, vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6388-1_21
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DOI: https://doi.org/10.1007/978-1-4757-6388-1_21
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