A Generalized Return Vector for Projection Methods in Optimization With Nonlinear Constraints

Variable metric methods can be adapted to constrained nonlinear optimization by incorporating projection methods and a return vector when the indicated next step leaves the feasible region. A generalized return vector is developed here which yields a superior return to the feasible region in terms of the metric associated with the objective function. It is shown that a better point results and faster convergence is expected. A numerical example is given.