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Nonlinear Programming

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Methods of Mathematical Economics

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

Look at the following problem:

$$\begin{array}{*{20}{c}} {A{\text{x}}\; = \;{\text{b,}}\;{\text{x}} \geqslant {\text{0}}} \\ {{\text{p}}\; \cdot \;{\text{x}}\;{\text{ + }}\frac{1}{2}{\text{x}}\; \cdot {\text{Cx}}\;{\text{ = }}\;{\text{minimum}}} \end{array}$$
(1)

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References

  1. Philip Wolfe, The Simplex Method for Quadratic Programming,Econometrica, vol. 27 (1959) pp. 382–398.

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  5. Fritz John, “Extremum Problems with Inequalities as Subsidiary Conditions,” Studies and Essays, Courant Anniversary Volume ( New York, Interscience, 1948 ), 187–204.

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  6. H. W. Kuhn, “Nonlinear Programming: a Historical View,” in R. W. Cottle and C. E. Lemke (ed.) Nonlinear Programming, SIAM-AMS Proceedings, Vol. 9 (1976) pp. 1–26.

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  7. M. Slater, “Lagrange Multipliers Revisited,” Cowles Commission Discussion Paper No. 403, November, 1950.

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  8. R. J. Duffin, E. L. Peterson, and Clarence Zener, Geometric Programming,1967, John Wiley and Sons.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, California Institute of Technology, 91125, Pasadena, CA, USA

    Joel Franklin

Authors
  1. Joel Franklin
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© 1980 Springer Science+Business Media New York

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Franklin, J. (1980). Nonlinear Programming. In: Methods of Mathematical Economics. Undergraduate Texts in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25317-5_2

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  • DOI: https://doi.org/10.1007/978-3-662-25317-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-90481-6

  • Online ISBN: 978-3-662-25317-5

  • eBook Packages: Springer Book Archive

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