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Dominating Sets for Convex Functions with Some Applications

Author

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  • E. Carrizosa

    (Universidad de Sevilla)

  • J. B. G. Frenk

    (Erasmus Universiteit Rotterdam)

Abstract

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this paper, we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the fields of linear regression and location.

Suggested Citation

  • E. Carrizosa & J. B. G. Frenk, 1998. "Dominating Sets for Convex Functions with Some Applications," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 281-295, February.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:2:d:10.1023_a:1022614029984
    DOI: 10.1023/A:1022614029984
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    References listed on IDEAS

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    Cited by:

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