Low-Rank Tensor Estimation via Generalized Norm/Quasi-Norm Difference Regularization

In this paper we study minimization of lp-q (0 < p ≤ 1, q ≥ 1, p ≠ q), the general difference of lp and lq norms/quasi-norms for solving nonconvex unconstrained nonlinear programming. We first establish an exact (stable) sparse recovery condition for the l_p-q constrained problem under a restrict...

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Bibliographic Details
Published in:	2018 4th International Conference on Big Data Computing and Communications (BIGCOM) pp. 144 - 149
Main Authors:	Cen, Yi, Cen, Yigang, Wang, Ke, Li, Jincong, Chen, Shiming, Zhang, Linnan, Tao, Dan
Format:	Conference Proceeding
Language:	English
Published:	IEEE 01.08.2018
Subjects:	Approximation algorithms difference of convex/nonconvex functions algorithm Estimation Iterative methods l_p-q-minimization l_p-q-null space property Minimization Optimization Sensors Tensile stress
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Summary:	In this paper we study minimization of lp-q (0 < p ≤ 1, q ≥ 1, p ≠ q), the general difference of lp and lq norms/quasi-norms for solving nonconvex unconstrained nonlinear programming. We first establish an exact (stable) sparse recovery condition for the l_p-q constrained problem under a restricted p-isometry property, and then propose an iterative algorithm for l_p-q regularized unconstrained minimization based on the t-variant of iterative reweighted minimization method (t ≥ 1) and ε-approximation. We theoretically prove that the proposed algorithm converges to a stationary point satisfying the first-order optimality condition. Our extensive real-image experiment results demonstrate that if the sensing operator satisfies the restricted p-isometry property, the proposed iterative reweighted minimization method for l_p-q unconstraint problem generally outperforms the existing methods (especially for those methods based on the difference of norms).
DOI:	10.1109/BIGCOM.2018.00030