Convergence rates of symplectic Pontryagin approximations in optimal control theory

Convergence Rates of Symplectic Pontryagin Approximations in Optimal Control Theory ∗

Many inverse problems for differential equations can be formulated as optimal control problems. It is well known that inverse problems often need to be regularized to obtain good approximations. This work presents a systematic method to regularize and to establish error estimates for approximations to some control problems in high dimension, based on symplectic approximation of the Hamiltonian ...

Pontryagin Maximum Principle for Optimal Control of

In this paper we investigate optimal control problems governed by variational inequalities. We present a method for deriving optimality conditions in the form of Pontryagin's principle. The main tools used are the Ekeland's variational principle combined with penalization and spike variation techniques. 1. Introduction. The purpose of this paper is to present a method for deriving a Pontryagin ...

Potential theory and optimal convergence rates in fast nonlinear diffusion ?

A potential theoretic comparison technique is developed, which yields the conjectured optimal rate of convergence as t → ∞ for solutions of the fast diffusion equation ut = ∆(u), (n− 2)+/n < m ≤ n/(n+ 2), u, t ≥ 0, x ∈ R, n ≥ 1 to a spreading self-similar profile, starting from integrable initial data with sufficiently small tails. This 1/t rate is achieved uniformly in relative error, and in w...

Rates of Convergence for Variable Resolution Schemes in Optimal Control

Extended Applicability of the Symplectic Pontryagin Method

Abstract. The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without the previous assumption on a bounded gradient of the discrete dual variable. The convergence proof uses the representation of solutions to a Hamilton...