Nonlinear Programming

  • Joel Franklin
Part of the Undergraduate Texts in Mathematics book series (UTM)

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)

Keywords

Entropy Hull Volatility Summing Vince 

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References

  1. Philip Wolfe, The Simplex Method for Quadratic Programming,Econometrica, vol. 27 (1959) pp. 382–398.Google Scholar
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    H. W. Kuhn and A. W. Tucker, “Nonlinear Programming,” in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability ( Berkeley, U. of California Press, 1950 ), 481–492.Google Scholar
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    William Karush, “Minima of Functions of Several Variables with Inequalities as Side Conditions,” Master’s Thesis, Department of Mathematics, University of Chicago, December, 1939, 26 pp.Google Scholar
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    Fritz John, “Extremum Problems with Inequalities as Subsidiary Conditions,” Studies and Essays, Courant Anniversary Volume ( New York, Interscience, 1948 ), 187–204.Google Scholar
  6. 4.
    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.Google Scholar
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    M. Slater, “Lagrange Multipliers Revisited,” Cowles Commission Discussion Paper No. 403, November, 1950.Google Scholar
  8. R. J. Duffin, E. L. Peterson, and Clarence Zener, Geometric Programming,1967, John Wiley and Sons.Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Joel Franklin
    • 1
  1. 1.Department of Applied MathematicsCalifornia Institute of TechnologyPasadenaUSA

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