Iterative Reweighted Minimization for Generalized Norm/Quasi-Norm Difference Regularized Unconstrained Nonlinear Programming

In this paper, we study the minimization of l p-q (0 <; p ≤ 1, q ≥ 1, p=6q), the general difference of l p and l q norms/quasi-norms, as a nonconvex metric for solving unconstrained nonlinear programming. We first establish an exact (stable) sparse recovery condition for the l p-q constrained pro...

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Bibliographic Details
Published in:	IEEE access Vol. 7; pp. 153102 - 153122
Main Authors:	Cen, Yi, Zhang, Linna, Wang, Ke, Cen, Yigang
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">lₚ –<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">q -minimization <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">lₚ –<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">q -null space property Algorithms Approximation algorithms Convergence Difference of convex/nonconvex functions algorithm Iterative algorithms Iterative methods iterative reweighted <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">lₜ minimization Measurement Methods Minimization Nonlinear programming Norms Optimization Recovery Sensors
ISSN:	2169-3536, 2169-3536
Online Access:	Get full text
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