In this paper we propose a general mathematical approach to existence of production equilibria in general economic model with incomplete assets markets, based on mathematical programming theory. In the first part, we demonstrate the existence of a General Equilibrium with Incomplete markets (GEl)}. In the second part, we introduce a concept of local equilibrium and we characterize such an equilibrium as the solution of a nonlinear system of equations. This system is very useful in practice since we avoid to compute the excess demand function that is difficult to obtain in large applied models. Furthermore, our characterization only requires limited short-selling and convexity assumptions at the neighborhood of the solution point. Finally, we also propose an algorithm for computing equilibria by interior point methods and we present numerical examples
