Affine minorants minimizing the sum of convex functions

  • L. McLinden
Contributed Papers

Abstract

It is often possible to replace a convex minimization problem by an equivalent one, in which each of the original convex functions is replaced by a suitably chosen affine minorant. In this paper we identify essentially the minimal conditions permitting this replacement, and also shed light on the close and complete link between such optimal affine minorants and certain optimal dual vectors. An application to the ordinary convex programming problem is included.

Key Words

Affine minorants Lagrange multipliers inf-convolution 

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References

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • L. McLinden
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbana

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