The stability number for a given graph G is the size of a maximum stable set in G. The Lovasz theta number provides an upper bound on the stability number and can be computed as the optimal value of the Lovasz semidefinite program. In this paper, we show that restricting the matrix variable in the Lovasz semidefinite program to be rank-one or rank-two yields a pair of continuous, nonlinear optimization problems each having the global optimal value equal to the stability number. We propose heuristics for obtaining large stable sets in G based on these new formulations and present computational results indicating the effectiveness of the heuristics.