In this paper, we consider high-dimensional nonconvexsquare-root-loss regressionproblems and introduce a proximal majorization-minimization (PMM) algorithm for solving these problems. Our key idea for making the pro...
详细信息
In this paper, we consider high-dimensional nonconvexsquare-root-loss regressionproblems and introduce a proximal majorization-minimization (PMM) algorithm for solving these problems. Our key idea for making the proposed PMM to be efficient is to develop a sparse semismooth Newton method to solve the corresponding subproblems. By using the Kurdyka-Lojasiewicz property exhibited in the underlining problems, we prove that the PMM algorithm converges to a d-stationary point. We also analyze the oracle property of the initial subproblem used in our algorithm. Extensive numerical experiments are presented to demonstrate the high efficiency of the proposed PMM algorithm.
In this paper, we consider high-dimensional nonconvexsquare-root-loss regressionproblems and introduce a proximal majorization-minimization (PMM) algorithm for solving these problems. Our key idea for making the pro...
详细信息
In this paper, we consider high-dimensional nonconvexsquare-root-loss regressionproblems and introduce a proximal majorization-minimization (PMM) algorithm for solving these problems. Our key idea for making the proposed PMM to be efficient is to develop a sparse semismooth Newton method to solve the corresponding subproblems. By using the Kurdyka-Łojasiewicz property exhibited in the underlining problems, we prove that the PMM algorithm converges to a d-stationary point. We also analyze the oracle property of the initial subproblem used in our algorithm. Extensive numerical experiments are presented to demonstrate the high efficiency of the proposed PMM algorithm.
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