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Many recent advances in multiple target tracking aim at finding a (nearly) optimal set of trajectories within a temporal window. To handle the large space of possible trajectory hypotheses, it is typically reduced to a finite set by some form of data-driven or regular discretization. In this work, we propose an alternative formulation of multitarget tracking as minimization of a continuous energy. Contrary to recent approaches, we focus on designing an energy that corresponds to a more complete representation of the problem, rather than one that is amenable to global optimization. Besides the image evidence, the energy function takes into account physical constraints, such as target dynamics, mutual exclusion, and track persistence. In addition, partial image evidence is handled with explicit occlusion reasoning, and different targets are disambiguated with an appearance model. To nevertheless find strong local minima of the proposed nonconvex energy, we construct a suitable optimization scheme that alternates between continuous conjugate gradient descent and discrete transdimensional jump moves. These moves, which are executed such that they always reduce the energy, allow the search to escape weak minima and explore a much larger portion of the search space of varying dimensionality. We demonstrate the validity of our approach with an extensive quantitative evaluation on several public data sets.