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A proximal MM method for the zero-norm regularized PLQ composite optimization problem
Dongdong Zhang, Shaohua Pan, Shujun Bi
This paper is concerned with a class of zero-norm regularized piecewise linear-quadratic (PLQ) composite minimization problems, which covers the zero-norm regularized -loss…
A proximal dual semismooth Newton method for computing zero-norm penalized QR estimator
Dongdong Zhang, Shaohua Pan, Shujun Bi
This paper is concerned with the computation of the high-dimensional zero-norm penalized quantile regression estimator, defined as a global minimizer of the zero-norm penalized che…
Several classes of stationary points for rank regularized minimization problems
Yulan Liu, Shaohua Pan
For the rank regularized minimization problem, we introduce several kinds of stationary points by the problem itself and its equivalent reformulations including the mathematical pr…
KL property of exponent of quadratic functions under nonnegative zero-norm constraints and applications
Shaohua Pan, Yuqia Wu, Shujun Bi
This paper focuses on the quadratic optimization over two classes of nonnegative zero-norm constraints: nonnegative zero-norm sphere constraint and zero-norm simplex constraint, wh…
Kurdyka-Lojasiewicz Property of Zero-Norm Composite Functions
Yuqia Wu, Shaohua Pan, Shujun Bi
This paper focuses on a class of zero-norm composite optimization problems. For this class of nonconvex nonsmooth problems, we establish the Kurdyka-Lojasiewicz property of exponen…
Calibrated zero-norm regularized LS estimator for high-dimensional error-in-variables regression
Ting Tao, Shaohua Pan, Shujun Bi
This paper is concerned with high-dimensional error-in-variables regression that aims at identifying a small number of important interpretable factors for corrupted data from many…