Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems

The Inexact Restoration method for Euler discretization of state and control constrained optimal control problems is studied. Convergence of the discretized (finite-dimensional optimization) problem to an approximate solution using the Inexact Restoration method and convergence of the approximate so...

Full description

Saved in:
Bibliographic Details
Published in:Journal of optimization theory and applications 2013-03, Vol.156 (3), p.726-760
Main Authors: Banihashemi, Nahid, Yalçın Kaya, C.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Convergence
Discretization
Engineering
Eulers equations
Experiments
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimal control
Optimization
Optimization algorithms
Restoration
Robots
Studies
Theory of Computation
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Inexact Restoration method for Euler discretization of state and control constrained optimal control problems is studied. Convergence of the discretized (finite-dimensional optimization) problem to an approximate solution using the Inexact Restoration method and convergence of the approximate solution to a continuous-time solution of the original problem are established. It is proved that a sufficient condition for convergence of the Inexact Restoration method is guaranteed to hold for the constrained optimal control problem. Numerical experiments employing the modelling language AMPL and optimization software Ipopt are carried out to illustrate the robustness of the Inexact Restoration method by means of two computationally challenging optimal control problems, one involving a container crane and the other a free-flying robot. The experiments interestingly demonstrate that one might be better-off using Ipopt as part of the Inexact Restoration method (in its subproblems) rather than using Ipopt directly on its own.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0140-4