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An optimal bound for d.c. programs with convex constraints

Author

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  • Emilio Carrizosa

Abstract

A well-known strategy for obtaining a lower bound on the minimum of a d.c. function f−g over a compact convex set S⊂ℝ n consists of replacing the convex function f by a linear minorant at x 0 ∈S. In this note we show that the x 0 * giving the optimal bound can be obtained by solving a convex minimization program, which corresponds to a Lagrangian decomposition of the problem. Moreover, if S is a simplex, the optimal Lagrangian multiplier can be obtained by solving a system of n + 1 linear equations. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Emilio Carrizosa, 2001. "An optimal bound for d.c. programs with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 47-51, October.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:1:p:47-51
    DOI: 10.1007/PL00003997
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    Cited by:

    1. Tammy Drezner & Zvi Drezner, 2011. "A note on equity across groups in facility location," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 705-711, October.
    2. Zvi Drezner & Carlton Scott, 2013. "Location of a distribution center for a perishable product," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 301-314, December.

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