Minimization of the k-th maximum and its application on LMS regression and VaR optimization&star

X Huang, J Xu, S Wang and C Xu
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X Huang: Tsinghua University and Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, P.R. China
J Xu: Tsinghua University and Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, P.R. China
S Wang: Tsinghua University and Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing, P.R. China
C Xu: Chiba Institute of Technology, Chiba, Japan

Journal of the Operational Research Society, 2012, vol. 63, issue 11, 1479-1491

Abstract: Motivated by two important problems, the least median of squares (LMS) regression and value-at-risk (VaR) optimization, this paper considers the problem of minimizing the k-th maximum for linear functions. For this study, a sufficient and necessary condition of local optimality is given. From this condition and other properties, we propose an algorithm that uses linear programming technique. The algorithm is assessed on real data sets and the experiments for LMS regression and VaR optimization both show its effectiveness.

Date: 2012
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