Journal of Optimization Theory and Applications

, Volume 23, Issue 3, pp 389–400 | Cite as

Sufficient conditions for duality in homogeneous programming

  • M. Schechter
Contributed Papers


A symmetric duality theory for programming problems with homogeneous objective functions was published in 1961 by Eisenberg and has been used by a number of authors since in establishing duality theorems for specific problems. In this paper, we study a generalization of Eisenberg's problem from the viewpoint of Rockafellar's very general perturbation theory of duality. The extension of Eisenberg's sufficient conditions appears as a special case of a much more general criterion for the existence of optimal vectors and lack of a duality gap. We give examples where Eisenberg's sufficient condition is not satisfied, yet optimal vectors exist, and primal and dual problems have the same value.

Key Words

Duality mathematical programming homogeneous functions subgradients 


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Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • M. Schechter
    • 1
    • 2
  1. 1.Department of MathematicsLehigh UniversityBethlehem
  2. 2.Department of Applied MathematicsTechnion—IIT, Technion CityHaifaIsrael

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