NDLI: Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation

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Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation

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Volume 10 (2016) : Issue 2, Apr

Volume 10 (2016) : Issue 1, Feb

IET Wireless Sensor Systems

Micro & Nano Letters

The Journal of Engineering

Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation

Content Provider	IET Digital Library
Author	Yang, Zhijing Kuang, Wei Chao Ling, Bingo Wing Kuen Dai, Qingyun
Abstract	This study proposes an iterative method to approximate an N-dimensional optimisation problem with a weighted Lp norm and L2 norm objective function by a sequence of N independent one-dimensional optimisation problems. This iterative method is inspired by the existing weighted L1 norm and L2 norm separable surrogate functional (SSF) iterative shrinkage algorithm. However, as these independent one-dimensional optimisation problems consist of weighted Lp norm and L2 norm objective functions, these optimisation problems are non-convex and they may have more than one locally optimal solutions. In general, it is very difficult to find their globally optimal solutions. To address this difficulty, this study proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. In this case, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem.
Starting Page	247
Ending Page	253
Page Count	7
ISSN	17519675
Volume Number	10
e-ISSN	17519683
Issue Number	Issue 3, May (2016)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/10/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2014.0234
Journal	IET Signal Processing
Publisher Date	2016-05-01
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Concave Programming Constraint Transcription Method Linear Functional Inequality Constraint Linear Objective Function Linear Programming Maximum Total Absolute Value Minimization Minimisation Nonconvex Functional Equality Constraint Nonsmooth Nonconvex Functional Constrained Optimisation Optimisation Technique Positivity Constraint Pth-order Derivatives Signal Instantaneous Frequency Representation Signal Instantaneous Magnitude Representation Signal Processing Signal Processing And Detection Signal Processing Theory
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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