Funções Invexas Diferenciáveis e o Teorema de Karush-Kuhn-Tucker1

Authors

  • J. Cervelati
  • M.A. Rojas Medar

DOI:

https://doi.org/10.5540/tema.2006.07.01.0053

Abstract

Em 1980 surgiu o conceito de função invexa, esta classe de funções é maior do que a classe de funções convexas. Após esta descoberta, vários estudos foram feitos no intuito de utilizar esta nova classe de funções para garantir otimalidade para problemas de Programação Matemática. O objetivo deste trabalho é mostrar que as Condições de Karush-Kuhn-Tucker garantem otimalidade global se todas as funções do problema forem, ao invés de convexas, invexas.

References

[1] R. Barbolla, E. Cerdá e P. Sanz, “Optimización. Cuestiones, Ejercicios y Aplicaciones a la Economia”. Prentice Hall, Madrid, 2000.

A.J. Brandão, M.A. Rojas-Medar e G.N. Silva, Uma introdução às funções invexas diferenciáveis com aplicações em otimização. Boletim da Sociedade Paranaense de Matemática, 19, No. 1-2 (1999), 51-65.

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B.D. Craven, Invex functions and constrained local minima. Bull. Austral.Math. Soc., 24 (1981), 357-366.

G. Giorgi, A note on the relashionships between convexity and invexity. J. Austral. Math. Soc. Ser. B, 32 (1990), 97-99.

M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl., 80 (1981), 545-550.

O.L. Mangasarian, Nonlinear Programming. Classics in Applied Mathematics, SIAM, 10, 1994.

D.H. Martin, The essence of invexity. J. Math. Anal. Appl., 47 (1985), 65-76.

A.C. Moretti e M.A. Rojas-Medar, Condiciones suficientes de optimalidad em programación no lineal. Cubo Matemática Educacional, 3, No. 2 (2001), 129-146.

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Published

2006-06-01

How to Cite

Cervelati, J., & Rojas Medar, M. (2006). Funções Invexas Diferenciáveis e o Teorema de Karush-Kuhn-Tucker1. Trends in Computational and Applied Mathematics, 7(1), 53–61. https://doi.org/10.5540/tema.2006.07.01.0053

Issue

Vol. 7 No. 1 (2006)

Section

Original Article

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