A proven approach for unconstrained minimization of a function, f(x), x ∈ ℜ n , is to build and solve a quadratic model at a local estimate x (k) i.e. apply the trust region method. In this paper we propose a direct extension of this modeling approach to constrained minimization. A local quadratic model of both the objective function and the constraints is built. This model is too hard to solve, so it is relaxed using the Lagrangian dual, which is then solved by semidefinite programming techniques. The key ingredient in this approach is the equivalence between the Lagrangian and semidefinite relaxations.