Abstract
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 equililibrium problems, is given.
Implicit function formulas for differentiating the unique solution of a system of simultaneous inequalities are also derived.
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Bigelow, J.H., Shapiro, N.Z. Implicit function theorems for mathematical programming and for systems of inequalities. Mathematical Programming 6, 141–156 (1974). https://doi.org/10.1007/BF01580232
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DOI: https://doi.org/10.1007/BF01580232