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In this work we deal with exponential sum models coming from data acquisition in the empirical sciences. We present a two step approach based on Tikhonov regularization and combinatorial optimization, to obtain stable parameter estimations, which fit the data. We develop properties of the solutions, based on their optimality conditions. Some numerical experiments are shown to illustrate our approach

A mixed integer nonlinear programming formulation for the problem of fitting positive exponential sums to empiricaldata