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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. [ABSTRACT FROM AUTHOR]

In this paper, we consider distributed estimation of a noise-corrupted deterministic parameter in energy-constrained wireless sensor networks from energy-distortion perspective. Given a total energy budget allowable to be used by all sensors, there exists a tradeoff between the subset of active sensors and the energy used by each active sensor in order to minimize the estimation MSE. To determine the optimal quantization bit rate and transmission energy of each sensor, a concept of equivalent unit-energy MSE function is introduced. Based on this concept, an optimal energy-constrained distributed estimation algorithm for homogeneous sensor networks and a quasi-optimal energy-constrained distributed estimation algorithm for heterogeneous sensor networks are proposed. Moreover, the theoretical energy-distortion performance bound for distributed estimation is addressed and it is shown that the proposed algorithm is quasi-optimal within a factor 2 of the theoretical lower bound. Simulation results also show that the proposed method can achieve a significant reduction in the estimation MSE when compared with other uniform schemes. Finally, the proposed algorithm is easy to implement in a distributed manner and it adapts well to the dynamic sensor environments. [ABSTRACT FROM AUTHOR]