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We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.