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Generalized reduced gradient method as an extension of feasible direction methods

  • Y. Smeers
Contributed Papers

Abstract

The paper presents modifications of the generalized reduced gradient method which allows for a convergence proof. For that, a special construction of the basis is introduced, and some tools of the theory of feasible direction are used to modify the common choice of the direction at every step.

Key Words

Mathematical programming nonlinear programming gradient methods feasible direction methods convergence 

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References

  1. 1.
    Wolfe, P.,An Extended Simplex Method, Notices of the American Mathematical Society, Vol. 9, No. 4, 1962.Google Scholar
  2. 2.
    Wolfe, P.,On the Convergence of Gradient Methods under Constraints, IBM Journal of Research and Development, Vol. 19, No. 4, 1972.Google Scholar
  3. 3.
    Zangwill, W.,The Convex-Simplex Method, Management Science, Vol. 14, No. 3, 1967.Google Scholar
  4. 4.
    Zangwill, W.,Nonlinear Programming: A Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.Google Scholar
  5. 5.
    Faure, P., andHuard, P.,Résolution de Programmes Mathématiques à Fonction Nonlinéaire par la Méthode du Gradient Réduit, Revue Française de Recherche Opérationnelle, Vol. 9, No. 36, 1965.Google Scholar
  6. 6.
    Huard, P.,Convergence of the Reduced Gradient Method, Paper presented at the Nonlinear Programming Symposium, Madison, Wisconsin, 1974.Google Scholar
  7. 7.
    Cabay, D., andLuenberger, D G.,Efficiently Converging Methods for Nonlinear Constrained Minimization Methods Based on the Reduced Gradient, SIAM Journal on Control and Optimization, Vol. 14, No. 1, 1976.Google Scholar
  8. 8.
    Abadie, J., andCarpentier, J.,Généralisation de la Méthode du Gradient Réduit de Wolfe au Cas de Contraintes Nonlinéaires, Proceedings of the IFORS Congress, Cambridge, Massachusetts, 1966.Google Scholar
  9. 9.
    Gochet, W., Loute, E., andSolow, W.,Comparative Computer Results of Three Algorithms for Solving Prototype Geometric Programming Problems, Cahier du Centre d'Etudes de Recherche Opérationnelle, Vol. 16, No. 4, 1974.Google Scholar
  10. 10.
    Himmelblau, D.,Applied Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1972.Google Scholar
  11. 11.
    Smeers, Y.,A Convergence Proof of a Special Version of the Generalized Reduced Gradient Method (GRGS), Revue Française d'Automatique, Informatique, et Recherche Opérationnelle, Vol. 5, No. 3, 1974.Google Scholar
  12. 12.
    Abadie, J., andCarpentier, J.,Generalization of the Wolfe Reduced Gradient Method to the Case of Nonlinear Constraints, Optimization, Edited by R. Fletcher, Academic Press, London, England, 1969.Google Scholar
  13. 13.
    Hadley, G.,Linear Algebra, Addision-Wesley Publishing Company, Reading, Massachusetts, 1961.Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • Y. Smeers
    • 1
  1. 1.Department of Engineering and CORECatholic University of LouvainLouvainBelgium

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