5,506 research outputs found
A Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel
This paper presents an optimization approach for a system consisting of
multiple bidirectional links over a two-way amplify-and-forward relay. It is
desired to improve the fairness of the system. All user pairs exchange
information over one relay station with multiple antennas. Due to the joint
transmission to all users, the users are subject to mutual interference. A
mitigation of the interference can be achieved by max-min fair precoding
optimization where the relay is subject to a sum power constraint. The
resulting optimization problem is non-convex. This paper proposes a novel
iterative and low complexity approach based on a modified Levenberg-Marquardt
method to find near optimal solutions. The presented method finds solutions
close to the standard convex-solver based relaxation approach.Comment: submitted to IEEE Transactions on Vehicular Technology We corrected
small mistakes in the proof of Lemma 2 and Proposition
Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems
The Levenberg–Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst-case iteration complexity rate, and a guaranteed rate of local convergence for both zero and nonzero small residual problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt method that matches, simultaneously, the state of the art in all of these convergence properties with a single seamless algorithm. Numerical experiments confirm the theoretical behavior of our proposed algorithm
A Hybrid Global Minimization Scheme for Accurate Source Localization in Sensor Networks
We consider the localization problem of multiple wideband sources in a
multi-path environment by coherently taking into account the attenuation
characteristics and the time delays in the reception of the signal. Our
proposed method leaves the space for unavailability of an accurate signal
attenuation model in the environment by considering the model as an unknown
function with reasonable prior assumptions about its functional space. Such
approach is capable of enhancing the localization performance compared to only
utilizing the signal attenuation information or the time delays. In this paper,
the localization problem is modeled as a cost function in terms of the source
locations, attenuation model parameters and the multi-path parameters. To
globally perform the minimization, we propose a hybrid algorithm combining the
differential evolution algorithm with the Levenberg-Marquardt algorithm.
Besides the proposed combination of optimization schemes, supporting the
technical details such as closed forms of cost function sensitivity matrices
are provided. Finally, the validity of the proposed method is examined in
several localization scenarios, taking into account the noise in the
environment, the multi-path phenomenon and considering the sensors not being
synchronized
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