Implicit Function Theorems for Optimization Problems and for Systems of Inequalities

by James H. Bigelow, Norman Shapiro


Full Document

FormatFile SizeNotes
PDF file 0.9 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback34 pages $20.00 $16.00 20% Web Discount

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.

This report is part of the RAND Corporation report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.