Implicit Function Theorems for Optimization Problems and for Systems of Inequalities

by James H. Bigelow, Norman Shapiro

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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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