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A natural extension of the classical envelope theorem in vector differential programming

Author

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  • F. García Castaño
  • M. Melguizo Padial

Abstract

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • F. García Castaño & M. Melguizo Padial, 2015. "A natural extension of the classical envelope theorem in vector differential programming," Journal of Global Optimization, Springer, vol. 63(4), pages 757-775, December.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:4:p:757-775
    DOI: 10.1007/s10898-015-0307-2
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    References listed on IDEAS

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    4. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    5. Harold Hotelling, 1932. "Edgeworth's Taxation Paradox and the Nature of Demand and Supply Functions," Journal of Political Economy, University of Chicago Press, vol. 40(5), pages 577-577.
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