We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indiﬀerence points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem: ﬁrst-order conditions are necessary at interior optimal choices. We only assume diﬀerentiability of the utility function with respect to the continuous choices. The continuous choice may be from any Banach space and the discrete choice from any non-empty set.
|Number of pages||24|
|Publication status||Published - Apr 2012|