Implicit Function Theorems for Optimization Problems and for Systems of Inequalities

James H. Bigelow, Norman Shapiro

ResearchPublished 1974

Implicit function formulas for differentiating the solutions of mathematical programming problems satisfying the conditions of the Kuhn-Tucker theorem are motivated and rigorously demonstrated. The special case of a convex objective function with linear constraints is also treated with emphasis on computational details. An example, an application to chemical equilibrium problems, is given. Implicit function formulas for differentiating the unique solution of a system of simultaneous inequalities are also derived.

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  • Copyright: RAND Corporation
  • Availability: Available
  • Year: 1974
  • Print Format: Paperback
  • Paperback Pages: 34
  • Paperback Price: $20.00
  • Document Number: R-1036-PR

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RAND Style Manual
Bigelow, James H. and Norman Shapiro, Implicit Function Theorems for Optimization Problems and for Systems of Inequalities, RAND Corporation, R-1036-PR, 1974. As of September 23, 2024: https://www.rand.org/pubs/reports/R1036.html
Chicago Manual of Style
Bigelow, James H. and Norman Shapiro, Implicit Function Theorems for Optimization Problems and for Systems of Inequalities. Santa Monica, CA: RAND Corporation, 1974. https://www.rand.org/pubs/reports/R1036.html. Also available in print form.
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