Envelope Theorems for Arbitrary Choice Sets
研究任意选择集下的优化问题，证明传统包络公式在值函数可微点成立，并给出值函数绝对连续、左右可微或完全可微的条件，适用于机制设计、凸规划、连续优化、鞍点问题、参数化约束问题和最优停止问题。
The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative.This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function.We also provide conditions for the value function to be, variously, absolutely continuous, left-and right-differentiable, or fully differentiable.These results are applied to mechanism design, convex programming, continuous optimization problems, saddle-point problems, problems with parameterized constraints, and optimal stopping problems.