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Sur la convergence théorique de la méthode du gradient réduit généralisé

The theoritical convergence of generalized reduced gradient method

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Summary

The theoretical convergence of Generalized Reduced Gradient Method (GRG) has not been proved; the purpose of this paper is to propose two theoritical and general variants of the original method and a proof of their convergence.

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Rèfèrences

  1. Abadie, J., Carpentier, J.: Generalization of the Wolfe reduced gradient method to the case of nonlinear constraintes. In: Optimization (R. Fletcher, ed.) London: Academic 1969

    Google Scholar 

  2. Abadie, J., Guigou, J.: Méthode du gradient réduit généralisé: Publication de l'Electricité de France (EDF); Avril 1969

  3. Faure, P., Huard, P.: Résolution de programmes mathématiques à fonction nonlinéaire par la méthode du Gradient Réduit; Rev. Française Recherche Opérationnelle36, 167–206 (1965)

    Google Scholar 

  4. Huard, P.: Convergence of the reduced gradient method. In: Nonlinear programming symposium at Madison 1974; O.L. Mangasarian; R.R. Meyer; S.M. Robinson. (eds.) p. 29–54. New York-London: Academic 1975

    Google Scholar 

  5. Luenberger, D.G.: Introduction to linear and nonlinear programming. New York-London: Academic 1973

    Google Scholar 

  6. Mokhtar-Kharroubi, H.: Thèse 3ème cycle; Paris VI; Juin 1976. Chapitre V: Méthodes de gradient réduit

  7. Mokhtar-Kharroubi, H.: Sur quelques méthodes de gradient réduit sous contraintes linéaires; RAIRO-Analyse numerique V 13, N2, 167–180 (1979)

    Google Scholar 

  8. Smeers, Y.: Generalized reduced gradient method as an extension of feasible direction methods; J. Optimization Theory Appl.22, 209–226 (1977)

    Google Scholar 

  9. Wolfe, P.: Reduced gradient method; RAND Document Juin 1962

  10. Wolfe, P.: On the convergence of gradient method under constraintes; IBM Journal. 407–411 (1972)

  11. Zangwill, W.: The convex-simplex method; Management Sci.14, 221–238 (1967)

    Google Scholar 

  12. Zangwill, W.: Nonlinear programming; A unified approach. Englewood Cliffs, New Jersey: Prentice-Hall 1969

    Google Scholar 

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  1. Rue Bahloul-Beldjilali, Mascara, Algerie

    H. Mokhtar-Kharroubi

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  1. H. Mokhtar-Kharroubi
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Mokhtar-Kharroubi, H. Sur la convergence théorique de la méthode du gradient réduit généralisé. Numer. Math. 34, 73–85 (1980). https://doi.org/10.1007/BF01463999

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  • DOI: https://doi.org/10.1007/BF01463999

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