Comparative Dynamics via Envelope Methods in Variational Calculus
扩展了Samuelson的原始-对偶方法，应用于非自治变分问题，证明参数扰动对最优路径的定性影响可由广义斯拉茨基矩阵表示，并给出最优值函数凸性的充分条件。
The primal-dual methodology of Samuelson (1965) is extended and applied to a nonautonomous variational calculus problem with a fixed vector of initial stocks, fixed initial and terminal time values, a free vector of terminal stocks, and a time-independent vector of parameters. It is shown that if the solution of the variational problem is smooth enough, the qualitative effects of parameter perturbations on the entire optimal arcs can be represented by a generalized Slutsky-type matrix, which holds in integral form and is symmetric negative semidefinite. Sufficient conditions for the optimal value function to be convex in the parameters are also given.