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On the relation between concavity cuts and the surrogate dual for convex maximization problems

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Abstract

In this note we establish a relation between two bounds for convex maximization problems, the one based on a concavity cut, and the surrogate dual bound. Both bounds have been known in the literature for a few decades but, to the authors’ knowledge, the relation between them has not been previously observed in the literature.

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References

  1. Bricker D.L.: Bounding a class of nonconvex linearly-constrained resource allocation problems via the surrogate dual. Math. Program. 18, 68–83 (1980)

    Article  Google Scholar 

  2. Dür M., Horst R.: Lagrange duality and partitioning techniques in nonconvex global optimization. J. Optim. Theory Appl. 95, 347–369 (1997)

    Article  Google Scholar 

  3. Dür M.: A class of problems where dual bounds beat underestimation bounds. J. Glob. Optim. 22, 49–57 (2002)

    Article  Google Scholar 

  4. Falk J.E.: Lagrange multipliers and nonconvex programs. SIAM J. Control 7, 534–545 (1969)

    Article  Google Scholar 

  5. Hamami M., Jacobsen S.E.: Exhaustive nondegenerate conical processes for concave minimization on convex polytopes. Math. Oper. Res. 13, 479–487 (1988)

    Article  Google Scholar 

  6. Horst R., Tuy H.: Global Optimization: Deterministic Approaches, 2nd edn. Springer, Berlin (1993)

    Google Scholar 

  7. Horst R., Thoai N.V.: Duality bound methods in global optimization. In: Audet, C., Hansen, P., Savard, G. (eds) Essays and Surveys in Global Optimization, pp. 79–105. Springer, US (2005)

    Chapter  Google Scholar 

  8. Thoai N.V., Tuy H.: Convergent algorithm for minimizing a concave function. Math. Oper. Res. 5, 556–566 (1980)

    Article  Google Scholar 

  9. Tuy H.: Concave programming under linear constraints. Sov. Math. 5, 1437–1440 (1964)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria Informatica, Università di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy

    Marco Locatelli

  2. Dipartimento di Sistemi e Informatica, Università di Firenze, Via di Santa Marta, 3, 50139, Firenze, Italy

    Fabio Schoen

Authors
  1. Marco Locatelli
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  2. Fabio Schoen
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Corresponding author

Correspondence to Fabio Schoen.

Additional information

This paper is dedicated to the memory of Reiner Horst. He has been a guide, a teacher, a reference, a nice friend we all miss.

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Locatelli, M., Schoen, F. On the relation between concavity cuts and the surrogate dual for convex maximization problems. J Glob Optim 52, 411–421 (2012). https://doi.org/10.1007/s10898-011-9748-4

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  • DOI: https://doi.org/10.1007/s10898-011-9748-4

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