We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are ob...

The matrix exponential is a much-studied matrix function having many applications. The Fréchet derivative of the matrix exponential describes the first-order sensitivity of eA to perturbations in A and its norm determines a condition number for eA. Among the numerous methods for computing eA the scaling and squaring method is the most widely used. We show that the implementation of the method i...

We present shortest path maps that support min-link queries from any source point on a line segment to destination points in either a simple polygon or a polygonal domain (a polygon with holes). These structures are more versatile than the traditional shortest path map from a fixed source point, and we use them to compute the min-link Fréchet distance between two polygonal curves. In addition t...

We study in this paper the first-order behavior of value functions in parametric dynamic programming with linear constraints and nonconvex cost functions. By establishing an abstract result on the Fréchet subdifferential of value functions of parametric mathematical programming problems, some new formulas on the Fréchet subdifferential of value functions in parametric dynamic programming are ob...

We consider the Fréchet distance between two curves which are given as a sequence of m + n curved pieces. If these pieces are sufficiently well-behaved, we can compute the Fréchet distance in O(mn log(mn)) time. The decision version of the problem can be solved in O(mn) time.

We construct a Fréchet space as a subspace of Cω(Cn) where the Wick star product converges and is continuous. The resulting Fréchet algebra A~ is studied in detail including a ∗-representation of A~ in the Bargmann-Fock space and a discussion of star exponentials and coherent states.