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Generalized reduced gradient method as an extension of feasible direction methods. (English) Zbl 0336.65035

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] Wolfe, P.,An Extended Simplex Method, Notices of the American Mathematical Society, Vol. 9, No. 4, 1962. · Zbl 0109.14004
[2] Wolfe, P.,On the Convergence of Gradient Methods under Constraints, IBM Journal of Research and Development, Vol. 19, No. 4, 1972. · Zbl 0265.90046
[3] Zangwill, W.,The Convex-Simplex Method, Management Science, Vol. 14, No. 3, 1967. · Zbl 0153.49002
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[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.
[6] Huard, P.,Convergence of the Reduced Gradient Method, Paper presented at the Nonlinear Programming Symposium, Madison, Wisconsin, 1974.
[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.
[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.
[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. · Zbl 0294.90082
[10] Himmelblau, D.,Applied Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1972. · Zbl 0241.90051
[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.
[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. · Zbl 0254.90049
[13] Hadley, G.,Linear Algebra, Addision-Wesley Publishing Company, Reading, Massachusetts, 1961.
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