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On the Identification properties of a projected gradient method
No full textThe 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
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