On the Identification properties of a projected gradient method

The authors study the convergence properties of a projected gradient algorithm for the general problem min{f(x) x in R where f: R^n -> R is a mapping continuously differentiable on a closed convex set Q C R'. The algorithm, which requires only one projection per iteration, is a special version of the method of projection of the gradient by Demyanov and Rubinov [Approximate Methods in Optimization Problems, Elsevier, New York, 1970] where the step choice is made according to a scheme similar to the one used by Calamai and More [Math. Programming, 39 (1987), pp. 93-116]. The authors are mainly interested in analysing the identification property of the algorithm for the case where the set Q is a polyhedron, that is, the ability to identify in a finite number of steps the face in which the final solution lies. The convergence results that are shown are very similar to those shown in [6] for the standard projected gradient method.