Fast-Lipschitz optimization with wireless sensor networks applications

Motivated by the need for fast computations demanded by wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contr...

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Bibliographic Details
Published in:2011 10th International Conference on Information Processing in Sensor Networks Vol. 56; no. 10; pp. 378 - 389
Main Authors: Fischione, Carlo, Jonsson, Ulf
Format: Conference Proceeding Journal Article
Language:English
Published: New York IEEE 01.10.2011
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Series:Proceedings of the 10th ACM/IEEE International Conference on Information Processing in Sensor Networks, IPSN'11
Subjects:
Algorithms
Availability
Computation
Computational complexity
Convergence
Convergence of numerical methods
Convex and Non-convex Optimization
Convex optimization
Data processing
Distributed computations
Distributed Optimization
Interference
Interference Function Theory
Lagrange multipliers
Mathematical models
Methods
multi-objective optimization
Networks
Nonconvex optimization
Optimization
Parallel and Distributed Computation
Power control
Radio transmitters
Receivers
Sensors
Site selection
Studies
Wireless communication
Wireless sensor
Wireless Sensor Networks
ISBN:9781612848549, 1612848540
ISSN:0018-9286, 1558-2523, 1558-2523
Online Access:Get full text
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Summary:Motivated by the need for fast computations demanded by wireless sensor networks, the new F-Lipschitz optimization theory is introduced for a novel class of optimization problems. These problems are defined by simple qualifying properties specified in terms of increasing objective function and contractive constraints. It is shown that feasible F-Lipschitz problems have always a unique optimal solution that satisfies the constraints at equality. The solution is obtained quickly by asynchronous algorithms of certified convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization. Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized F-Lipschitz problems is at least superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditional La-grangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods. Examples of application of the new optimization method are given for distributed detection and radio power control in wireless sensor networks. The drawback of the F-Lipschitz optimization is that it might be difficult to check the qualifying properties. For more general optimization problems, it is suggested that it is convenient to have conditions ensuring that the solution satisfies the constraints at equality.
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ISBN:9781612848549
1612848540
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2011.2163855