Abstract
In this paper, we aim to find sparse solutions of the linear complementarity problems (LCPs), which has many applications such as bimatrix games and portfolio selection. Mathematically, the underlying model is NP-hard in general. Thus, an \(\ell _{1/2}\) regularized projection minimization model is proposed for relaxation. A half thresholding projection (HTP) algorithm is then designed for this regularization model, and the convergence of HTP algorithm is studied. Numerical results demonstrate that the HTP algorithm can effectively solve this regularization model and output very sparse solutions of LCPs with high quality.
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Acknowledgments
This research was supported by the National Natural Science Foundation of China (71271021,11001011,11431002), the Fundamental Research Funds for the Central Universities of China (2013JBZ005) and the Scientific Research Fund of Hebei Provincial Education Department (No. QN20132030)s. The authors are grateful to the referees for their valuable comments which improve the presentation of this paper.
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Shang, M., Zhang, C., Peng, D. et al. A half thresholding projection algorithm for sparse solutions of LCPs. Optim Lett 9, 1231–1245 (2015). https://doi.org/10.1007/s11590-014-0834-7
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DOI: https://doi.org/10.1007/s11590-014-0834-7