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Application of the Armijo stepsize rule to the solution of a nonlinear system of equalities and inequalities

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Abstract

In this paper, we present an application of the Armijo procedure to an algorithm for solving a nonlinear system of equalities and inequalities. The stepsize procedure contained in a quadratically convergent algorithm is replaced by an Armijo procedure on a nondifferentiable function, without any substantial extra computational work and without losing the quadratic rate of convergence. The use of the Armijo procedure on a nondifferentiable function opens the possibility of using it on nondifferentiable and minimax functions.

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References

  1. Restuccia, A., andGarcía-Palomares, U. M., AGlobal Quadratic Algorithm for Solving a System of Mixed Equalities and Inequalities, Mathematical Programming, Vol. 21, pp. 290–300, 1981.

    Google Scholar 

  2. Pshenichnyi, B. N.,Newton's Method for the Solution of Systems of Equalities and Inequalities, Mathematical Notes of the Academy of Sciences of USSR, Vol. 8, pp. 827–830, 1970.

    Google Scholar 

  3. Laserre, J. B.,Exact Penalty Functions and Lagrange Multipliers, RAIRO Automatique/Systems Analysis and Control, Vol. 14, pp. 117–125, 1980.

    Google Scholar 

  4. Bertsekas, D. P.,Necessary and Sufficient Conditions for a Penalty Method to be Exact, Mathematical Programming, Vol. 9, pp. 87–89, 1975.

    Google Scholar 

  5. Han, S. P., andMangasarian, O. L.,Exact Penalty Functions in Nonlinear Programming, Mathematical Programming, Vol. 17, pp. 251–269, 1979.

    Google Scholar 

  6. Restuccia, A., Estudio de un Algoritmo con Convergencia Global Para la Solución de un Problema de Programación Nolineal, Tesis de Magister en Ingeniería de Sistemas, Universidad Simón Bolívar, Caracas, Venezuela, 1979.

    Google Scholar 

  7. Malozemov, V. N., andDemyanov, V. F.,Introduction to Minimax, John Wiley and Sons, New York, New York, 1974.

    Google Scholar 

  8. Robinson, A.,Characterization of Stability in Linear Programming, Operations Research, Vol. 25, pp. 435–447, 1977.

    Google Scholar 

  9. Gauvin, J.,A Necessary and Sufficient Regularity Condition to Have Bounded Multipliers in Nonconvex Programming, Mathematical Programming, Vol. 12, pp. 136–138, 1977.

    Google Scholar 

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Authors and Affiliations

  1. Departmento de Procesos y Sistemas, Universidad Simón Bolivar, Caracas, Venezuela

    U. García-Palomares (Associate Professor)

  2. Departmento de Física, Universidad Simón Bolívar, Caracas, Venezuela

    A. Restuccia (Aggregate Professor)

Authors
  1. U. García-Palomares
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  2. A. Restuccia
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Additional information

Communicated by O. L. Mangasarian

The authors are indebted to one unknown referee who, through his comments, made this paper neater and more readable

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García-Palomares, U., Restuccia, A. Application of the Armijo stepsize rule to the solution of a nonlinear system of equalities and inequalities. J Optim Theory Appl 41, 405–415 (1983). https://doi.org/10.1007/BF00935360

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