We introduce a new model algorithm for solving nonlinear programming problems. At each iteration, the method solves (approximately) linearly constrained optimization problems. For this reason, it belongs to the class of SLCP (Sequential Linearly Constrained Programming) methods. Each iteration begins with a Restoration Phase, where feasibility of the current iterate is improved and follows with a Minimization Phase of Trust-Region type. In the Minimization Phase the objective function is reduced within an approximate (linearized) feasible set. The current point and the trial point obtained in the Minimization Phase are compared on the basis of a nonsmooth merit function that combines feasibility and optimality. We prove global convergence results.