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We propose to formulate multi-target tracking as minimization of a continuous energy function. Other than a number of recent approaches we focus on designing an energy function that represents the problem as faithfully as possible, rather than one that is amenable to elegant optimization. We then go on to construct a suitable optimization scheme to find strong local minima of the proposed energy. The scheme extends the conjugate gradient method with periodic trans-dimensional jumps. These moves allow the search to escape weak minima and explore a much larger portion of the variable-dimensional search space, while still always reducing the energy. To demonstrate the validity of this approach we present an extensive quantitative evaluation both on synthetic data and on six different real video sequences. In both cases we achieve a significant performance improvement over an extended Kalman filter baseline as well as an ILP-based state-of-the-art tracker.