A UNIQUENESS PROOF REGARDING THE SEQUENCE OF MULTIPLIERS GENERATED BY THE AUGMENTED LAGRANGIAN METHOD

Authors

  • Yna Rezza-Espinoza Facultad de Ingeniería Económica y Ciencias Sociales, Universidad Nacional de Ingeniería. Lima, Perú

Abstract

This paper presents a proof of the uniqueness of the sequence of multipliers generated by the Augmented Lagrangian Method with Penalties Pi ∈ P. This uniqueness has been proven over the last 25 years by using the equivalence relation between the Augmented Lagrangian and Proximal Point Methods.
Several researchers such as Rockafellar, Iusem and Gonzaga and Castillo proved this equivalence and the consequent uniqueness of the sequence of multipliers generated by the Augmented Lagrangian Method for particular cases. The proof we present includes all these cases and is also distinguished by being direct and not making use of the aforementioned equivalence relation.

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References

Bertsekas, D. P., Constrained Optimization and Lagrange Multiplier Method, Academic Press, New York, 1982.

Gonzaga, C. y Castillo, R., ”Métodos de Lagrangeano Aumentado usando Penalidades Generalizadas para Programação não linear'' Tesis, COPPE, UFRJ, 1998.

Hiriart - Urruty J.- Baptiste y Lemaréchal, C., Convex Analysis and Minimization Algorithms I, 1 ed. New York, Springer-Verlag, 1993.

Hiriart - Urruty J.- Baptiste y Lemaréchal, C., Convex Analysis and Minimization Algorithms II, 1 ed. New York, Springer-Verlag, 1993.

Hestenes, M., “Multiplier and Gradient Methods”, Jota, vol 4, pp. 303-320, 1969.

Iusem, A., Métodos de Ponto Proximal em Otimizacao, 20° Coloquio Brasileiro de Matemática , IMPA, R., J., Brasil, 1995.

Martinet, B., “Regularisation D’inequations variationnelle par approximations successives”, Revue Francaise de Informatiqué et Recherche Opérationelle 2, pp. 154 - 159, 1970.

Powell, M., “A method for nonlinear constraints in minimizations problems”, Ed., Academic Press, N.Y., pp. 283-298, 1969.

Rezza , Y., “Una prueba general de la buena definición del Método Lagrangeano Aumentado”, Revciuni, vol. 7, num. 1, pp. 38-57, 2003.

Rockafellar R. T., “Augmented Lagrangians and applications of the proximal point algorithm in convex programming”, Mathematics of Operations Research, vol. 1, pp. 97-116, 1976.

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Published

2004-02-01

How to Cite

Rezza-Espinoza, Y. (2004). A UNIQUENESS PROOF REGARDING THE SEQUENCE OF MULTIPLIERS GENERATED BY THE AUGMENTED LAGRANGIAN METHOD. Journal of the Science Faculty @ UNI, 8(1), 67–76. Retrieved from https://revistas.uni.edu.pe/index.php/revciuni/article/view/2377

Issue

Vol. 8 No. 1 (2004)

Section

Artículos

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