Optimal Impulse Control Problems and Linear Programming

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1 Citazioni (Scopus)

Abstract

Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. It turns out that any solution of the linear relaxation is a feasible solution for the optimal impulse control problem. Then, given the feasible solution, obtained solving the linear relaxation, we find the optimal solution via local search.
Lingua originaleEnglish
Numero di pagine5
Stato di pubblicazionePublished - 2009

All Science Journal Classification (ASJC) codes

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  • ???subjectarea.asjc.2600.2611???
  • ???subjectarea.asjc.2600.2606???

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