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A magnetic resonance device designed via global optimization techniques

Mathematical Programming volume 101, pages 339–364 (2004)Cite this article

Abstract.

In this paper we are concerned with the design of a small low-cost, low-field multipolar magnet for Magnetic Resonance Imaging with a high field uniformity. By introducing appropriate variables, the considered design problem is converted into a global optimization one. This latter problem is solved by means of a new derivative free global optimization method which is a distributed multi-start type algorithm controlled by means of a simulated annealing criterion. In particular, the proposed method employs, as local search engine, a derivative free procedure. Under reasonable assumptions, we prove that this local algorithm is attracted by global minimum points. Additionally, we show that the simulated annealing strategy is able to produce a suitable starting point in a finite number of steps with probability one.

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Authors and Affiliations

  1. Università di Roma “La Sapienza”, Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, via Buonarroti, 12, 00185, Roma, Italy

    Giampaolo Liuzzi, Stefano Lucidi & Veronica Piccialli

  2. INFM, Università de L’Aquila, Dipartimento di Tecnologie Biomediche, Coppito, 67100, L’Aq-uila, Italy

    Antonello Sotgiu

Authors
  1. Giampaolo Liuzzi
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  2. Stefano Lucidi
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  3. Veronica Piccialli
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  4. Antonello Sotgiu
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Corresponding author

Correspondence to Stefano Lucidi.

Additional information

This work was supported by CNR/MIUR Research Program “Metodi e sistemi di supporto alle decisioni”, Rome, Italy.

Mathematics Subject Classification (1991):65K05, 62K05, 90C56

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Liuzzi, G., Lucidi, S., Piccialli, V. et al. A magnetic resonance device designed via global optimization techniques. Math. Program., Ser. A 101, 339–364 (2004). https://doi.org/10.1007/s10107-004-0528-5

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  • DOI: https://doi.org/10.1007/s10107-004-0528-5

Key words

  • Magnetic Resonance Imaging
  • Global optimization
  • Simulated annealing
  • Derivative free methods