Greta Malaspina (University of Novi Sad, Serbia)

Title: A modified Levenberg-Maquardt method for large scale network adjustment

We present a numerical optimization approach for the solution of large scale Network Adjustment Problems that arise in localization problems such as GPS positioning, surveying and large scale Wireless Sensors Networks localization. We consider a modification of Levenberg Marquardt method that attempts to deal with the non-convex nature of the objective function and the large number of variables.
At each iteration of the classical method the search direction is computed by solving a linear system of equations, which is an expensive procedure when the number of unknowns in the problem that we consider is large, and represents the major obstacle to the solution of realistic, large scale, problems. We develop a scheme for the decomposition of the linear system, which consist in computing an approximation of the Levenberg Marquardt direction by solving a number of independent linear systems of smaller size, and we propose a correction strategy of the right sides that improves the quality of the approximated direction while retaining separability of the linear systems. The convergence analysis of the resulting method is studied under standard regularity assumptions of the objective function. Moreover, the algorithm we propose is tested on realistic adjustment problems and compared with Levenberg Marquardt in terms of both accuracy and computational cost.

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