6533b836fe1ef96bd12a0ad4

RESEARCH PRODUCT

Comparison of Numerical Methods in the Contrast Imaging Problem in NMR

Olivier CotsMathieu ClaeysPierre MartinonBernard Bonnard

subject

Optimization[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyMathematical optimization010103 numerical & computational mathematics02 engineering and technologyContrast imaging01 natural sciencesNuclear magnetic resonanceMagnetic resonance imaging020901 industrial engineering & automationSoftwareMaximum principleApplied mathematics0101 mathematicsGeometric programmingMathematicsbusiness.industryNumerical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]VectorsOptimal controlOptimal controlCalcul parallèle distribué et partagéMoment (mathematics)Direct methods[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]businessSoftware

description

International audience; In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach, and make a first step towards global optimality. Finally, some preliminary results are given in the bi-input case.

yearjournalcountryeditionlanguage
2013-12-01
https://hal.inria.fr/hal-00800436