Continuous-time linear programming problems revisited: A perturbation approach

Abstract

The class of continuous-time linear programming problems under the assumption that the constraints are satisfied almost everywhere in the time interval [0, T] is taken into account in this article. Under this assumption, its corresponding discretized problems cannot be formulated by equally dividing the time interval [0, T] as subintervals of [0, T] . In this article, we also introduce the perturbed continuous-time linear programming problems to prove the strong duality theorem when the constraints are assumed to be satisfied a.e. in [0, T] .

Keywords:

• continuous-time linear programming problems
• weak duality theorem
• strong duality theorem
• discretized problems
• perturbed optimization problems

AMS Subject Classifications::

• 90C05
• 90C46
• 90C90

Acknowledgements

The author would like to thank the associate editor for carefully reading the original manuscript and providing very useful suggestions which improved the presentation of this article.