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Mathematical Programming in Use pp 15–29Cite as

A family of iterative quadratic optimization algorithms for pairs of inequalities, with application in diagnostic radiology

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 9))

Abstract

We are concerned with systems of pairs of inequalities of the form γ≤(α, y)≤δ, where the dimensionality of the unknown vector y is typically 103 to 105. Such systems arise in certain problems in diagnostic radiology. We present and prove the convergence of a family of iterative algorithms for finding the feasible y with minimum norm. The algorithms are based on Hildreth’s quadratic optimization procedure for inequality constraints, but they exploit the special form of the feasible region to reduce significantly both computer time and storage.

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References

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Authors and Affiliations

  1. State University of New York at Buffalo, Amherst, NY, U.S.A.

    Gabor T. Herman & Arnold Lent

Authors
  1. Gabor T. Herman
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  2. Arnold Lent
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M. L. Balinski C. Lemarechal

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© 1978 The Mathematical Programming Society

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Herman, G.T., Lent, A. (1978). A family of iterative quadratic optimization algorithms for pairs of inequalities, with application in diagnostic radiology. In: Balinski, M.L., Lemarechal, C. (eds) Mathematical Programming in Use. Mathematical Programming Studies, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120823

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  • DOI: https://doi.org/10.1007/BFb0120823

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00795-8

  • Online ISBN: 978-3-642-00796-5

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