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In this paper we study linear-programming based approaches to the maximum matching problem in the semi-streaming model. In this model edges are presented sequentially, possibly in an adversarial order, and we are only allowed to use a small space. The allowed space is near linear in the number of vertices (and sublinear in the number of edges) of the input graph. The semi-streaming model is relevant in the context of processing of very large graphs. In recent years, there have been several new and exciting results in the semi-streaming model. However broad techniques such as linear programming have not been adapted to this model. In this paper we present several techniques to adapt and optimize linear-programming based approaches in the semi-streaming model. We use the maximum matching problem as a foil to demonstrate the effectiveness of adapting such tools in this model. As a consequence we improve almost all previous results on the semi-streaming maximum matching problem. We also prove new results on interesting variants.