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Minimizing the sum of linear fractional functions over the cone of positive semidefinite matrices: Approximation and applications |
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| Authors: | Yong Xia Longfei Wang Shu Wang |
| Affiliation: | 1. State Key Laboratory of Software Development Environment, LMIB of the Ministry of Education, School of Mathematics and System Sciences, Beihang University, Beijing, 100191, PR China;2. College of Science, North China Institute of Science and Technology, Hebei, 065201, PR China |
| Abstract: | The problem of maximizing the sum of two generalized Rayleigh quotients and the total least squares problem with nonsingular Tikhonov regularization are reformulated as a class of sum-of-linear-ratios minimizing over the cone of symmetric positive semidefinite matrices, which is shown to have a Fully Polynomial Time Approximation Scheme. |
| Keywords: | Fractional programming Semidefinite programming Rayleigh quotient Total least squares FPTAS |
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