Aggregated occupation measures and linear programming approach to constrained impulse control problems

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For a constrained optimal impulse control problem of an abstract dynamical system, we introduce the occupation measures along with the aggregated occupation measures and present two associated linear programs. We prove that the two linear programs are equivalent under appropriate conditions, and each linear program gives rise to an optimal strategy in the original impulse control problem. In particular, we show the absence of the relaxation gap. By means of an example, we also present a detailed comparison of the occupation measures and linear programs introduced here with the related notions in the literature.