Download This PaperOn the (Non-)Differentiability of the Optimal Value Function When the Optimal Solution Is Unique
31 Pages Posted: 31 Dec 2013 Last revised: 31 Jan 2018
Date Written: January 30, 2018
Abstract
We present examples of a parameterized optimization problem, with a continuous objective function differentiable with respect to the parameter, that admits a unique optimal solution, but whose optimal value function is not differentiable. We also show independence of Danskin's and Milgrom and Segal's envelope theorems.
Keywords: parameterized optimization, sensitivity analysis, value function, envelope theorem
JEL Classification: C61
Suggested Citation: Suggested Citation
Oyama, Daisuke and Takenawa, Tomoyuki, On the (Non-)Differentiability of the Optimal Value Function When the Optimal Solution Is Unique (January 30, 2018). Available at SSRN: https://ssrn.com/abstract=2373092 or http://dx.doi.org/10.2139/ssrn.2373092
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