Abstract. An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits regions in which the gradient is small infinitely often. Under certain unimodality assumptions, global convergence is established. In the quadratic case, a global linear rate of convergence is shown. The method is applied to distributed optimization problems arising in wireless sensor networks, and numerical experiments compare the new method with the standard incremental gradient method.
This paper addresses the problem of locating an acoustic source using a sensor network in a distributed manner, i.e., without transmitting the full data set to a central point for processing. This problem has been traditionally addressed through the nonlinear least squares or maximum likelihood framework. These methods, even though asymptotically optimal under certain conditions, pose a difficult global optimization problem. It is shown that the associated objective function may have multiple local optima and saddle points and hence any local search method might stagnate at a sub-optimal solution. In this paper, we formulate the problem as a convex feasibility problem and apply a distributed version of the projection onto convex sets (POCS) method. We give a closed form expression for the projection phase, which usually constitutes the heaviest computational aspect of POCS. Conditions are given under which, when the number of samples increases to infinity or in the absence of measurement noise, the convex feasibility problem has a unique solution at the true source location. In general, the method converges to a limit point or a limit cycle in the neighborhood of the true location. Simulation results show convergence to the global optimum with extremely fast convergence rates compared to the previous methods.
The problem of finding the maximum likelihood estimator of a commonly observed model, based on data collected by a sensor network under power and bandwidth constraints is considered. In particular, a case where the sensors cannot fully share their data is treated. An iterative algorithm that relaxes the requirement of sharing all the data is given. The algorithm is based on a local Fisher scoring method and an iterative information sharing procedure. The case where the sensors share sub-optimal estimates is also analyzed. The asymptotic distribution of the estimates is derived and used to provide means of discrimination between estimates that are associated with different local maxima of the loglikelihood function. The results are validated by a simulation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.