Discounted dynamic programming on Euclidean spaces

Constrained Discounted Dynamic Programming

This paper deals with constrained optimization of Markov Decision Processes with a countable state space, compact action sets, continuous transition probabilities, and upper semi-continuous reward functions. The objective is to maximize the expected total discounted reward for one reward function, under several inequality constraints on similar criteria with other reward functions. Suppose a fe...

Smooth Value and Policy Functions for Discounted Dynamic Programming

We consider a discounted dynamic program in which the spaces of states and actions are smooth (in a sense that is suitable for the problem at hand) manifolds. We give conditions that insure that the optimal policy and the value function are smooth functions of the state when the discount factor is small. In addition, these functions vary in a Lipschitz manner as the reward function-discount fac...

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

On Isometries of Euclidean Spaces

Metric Derivations on Euclidean and Non-euclidean Spaces

As introduced by Weaver, (metric) derivations extend the notion of differential operators on Euclidean spaces and provide a linear differentiation theory that is well-defined on all metric spaces with Borel measures. The main result of this paper is a rigidity theorem for measures on Euclidean spaces that support a maximal number of derivations. The proof relies substantially on ideas from geom...