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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…
Second-order optimality conditions for SDCMPCC and application to rank optimization problems
Yulan Liu, Shaohua Pan
This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints (SDCMPCC).To achieve this goal, we f…
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…
Subregularity of subdifferential mappings relative to the critical set and KL property of exponent 1/2
Shaohua Pan, Yulan Liu
For a proper extended real-valued function, this work focuses on the relationship between the subregularity of its subdifferential mapping relative to the critical set and its KL p…