A Two-Phase Model Algorithm with Global Convergence for Nonlinear Programming

. The family of feasible methods for minimization with nonlinear constraints includes Rosen's Nonlinear Projected Gradient Method, the Generalized Reduced Gradient Method (GRG) and many variants of the Sequential Gradient Restoration Algorithm (SGRA). Generally speaking, a particular iteration of any of these methods proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, generally a nonlinear system of equations. In the Minimization Phase, optimality is improved by means of the consideration of the objective function, or its Lagrangian, on the tangent subspace to the constraints. In this paper, minimal assumptions are stated on the Restoration Phase and the Minimization Phase that ensure that the resulting algorithm is globally convergent. The key point is the possibility of comparing two successive nonfeasible iterates by means of a suitable merit function that combines feasibility and optimality. The mer..