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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:2018 4th International Conference on Big Data Computing and Communications (BIGCOM) S. 144 - 149
Hauptverfasser: Cen, Yi, Cen, Yigang, Wang, Ke, Li, Jincong, Chen, Shiming, Zhang, Linnan, Tao, Dan
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.08.2018
Schlagworte:
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
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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