Normalized Incremental Subgradient Algorithm and Its Application

The problem of minimizing the sum of a number of component functions is of great importance in the real world. In this paper, a new incremental optimization algorithm, named normalized incremental subgradient (NIS) algorithm, is proposed for a class of such problems where the component functions hav...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 57; H. 10; S. 3759 - 3774
Hauptverfasser: Shi, Qingjiang, He, Chen, Jiang, Lingge
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.10.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Applied sciences
Bandwidth
Convergence
Convex feasibility problem
Detection, estimation, filtering, equalization, prediction
distributed maximum likelihood estimation
Energy measurement
Exact sciences and technology
Feasibility
Information, signal and communications theory
Iterative algorithms
Localization
Mathematical analysis
Mathematical models
Maximum likelihood estimation
Minima
Miscellaneous
node localization
normalized incremental subgradient algorithm
Optimization
Optimization methods
Particle measurements
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
source localization
Studies
Telecommunications and information theory
wireless sensor network
Wireless sensor networks
Performance evaluation
Wireless telecommunication
Gauss Newton method
wireless sensor network
Updating
Algorithm
Implementation
Optimization
Remote sensing
normalized incremental subgradient algorithm
Convex feasibility problem
Source localization
Signal processing
Wireless network
Numerical simulation
Feasibility
node localization
Maximum likelihood
Sensor array
distributed maximum likelihood estimation
Target detection
Signal detection
ISSN:1053-587X, 1941-0476
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Zusammenfassung:The problem of minimizing the sum of a number of component functions is of great importance in the real world. In this paper, a new incremental optimization algorithm, named normalized incremental subgradient (NIS) algorithm, is proposed for a class of such problems where the component functions have common local minima. The NIS algorithm is performed incrementally just as the general incremental subgradient (IS) algorithm and thus can be implemented in a distributed way. In the NIS algorithm, the update of each subiteration is based on a search direction obtained by individually normalizing each component of subgradients of component functions, resulting in much better convergence performance as compared to the IS algorithm and other traditional optimization methods (e.g., Gauss-Newton method). The convergence of the NIS algorithm with both diminishing stepsizes and constant stepsizes is proved and analyzed theoretically. Two important applications are presented. One is to solve a class of convex feasibility problems in a distributed way and the other is distributed maximum likelihood estimation. Numerical examples, arising from two important topics in the area of wireless sensor networks-source localization and node localization-demonstrate the effectiveness and efficiency of the NIS algorithm.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2009.2024901