4 citations · 12 across the 12 of their papers we have counts for
12 papers
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…
Error bound of critical points and KL property of exponent for squared F-norm regularized factorization
Ting Tao, Shaohua Pan, Shujun Bi
This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted…
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…
Equivalent Lipschitz surrogates for zero-norm and rank optimization problems
Yulan Liu, Shujun Bi, Shaohua Pan
This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent ma…
GEP-MSCRA for computing the group zero-norm regularized least squares estimator
Shujun Bi, Shaohua Pan
This paper concerns with the group zero-norm regularized least squares estimator which, in terms of the variational characterization of the zero-norm, can be obtained from a mathem…
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…
A multi-stage convex relaxation approach to noisy structured low-rank matrix recovery
Shujun Bi, Shaohua Pan, Defeng Sun
This paper concerns with a noisy structured low-rank matrix recovery problem which can be modeled as a structured rank minimization problem. We reformulate this problem as a mathem…
Error bounds for rank constrained optimization problems and applications
Shujun Bi, Shaohua Pan
This paper is concerned with the rank constrained optimization problem whose feasible set is the intersection of the rank constraint set $\mathcal{R}=\!\big\{X\in\mathbb{X}\ |\ {\r…
Exact penalty decomposition method for zero-norm minimization based on MPEC formulation
Shujun Bi, Xiaolan Liu, Shaohua Pan
We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the c…