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.

On the Identification properties of a projected gradient method

TORALDO, GERARDO
1993

Abstract

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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/441039
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? ND
social impact