Mathematical Programming: Series A and B
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Fitting brightness profiles of galaxies in one dimension is frequently done because it suffices for some applications and is simple to implement, but many studies now resort to two-dimensional fitting, because many well-resolved, nearby galaxies are often poorly fitted by standard one-dimensional models. For the fitting we use a model based on de Vaucoleurs and exponential functions that is represented as a set of concentric generalized ellipses that fit the brightness profile of the image. In the end, we have an artificial image that represents the light distribution in the real image, then we make a comparison between such artificial image and the original to measure how close the model is to the real image. The problem can be seen as an optimization problem because we need to minimize the difference between the original optical image and the model, following a normalized Euclidean distance. In this work we present a solution to such problem from a point of view of optimization using a hybrid algorithm, based on the combination of Evolution Strategies and the Quasi-Newton method. Results presented here show that the hybrid algorithm is very well suited to solve the problem, because it can find the solutions in almost all the cases and with a relatively low cost.